The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra

In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ying Chen [verfasserIn] Xiangyu Pan [verfasserIn] Yanyan Xu [verfasserIn] Guanggui Chen [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Wiener algebra approximation numbers Kolmogorov numbers entropy numbers

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 11(2023), 3974, p 3974
Übergeordnetes Werk:	volume:11 ; year:2023 ; number:3974, p 3974

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math11183974

Katalog-ID:	DOAJ093357834

Internformat


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520			\|a In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<.
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700	0		\|a Yanyan Xu \|e verfasserin \|4 aut
700	0		\|a Guanggui Chen \|e verfasserin \|4 aut
773	0	8	\|i In \|t Mathematics \|d MDPI AG, 2013 \|g 11(2023), 3974, p 3974 \|w (DE-627)737287764 \|w (DE-600)2704244-3 \|x 22277390 \|7 nnns
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allfields	10.3390/math11183974 doi (DE-627)DOAJ093357834 (DE-599)DOAJ8d6ec5fc8fa54345853fc7029f7fdebb DE-627 ger DE-627 rakwb eng QA1-939 Ying Chen verfasserin aut The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics Xiangyu Pan verfasserin aut Yanyan Xu verfasserin aut Guanggui Chen verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 3974, p 3974 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:3974, p 3974 https://doi.org/10.3390/math11183974 kostenfrei https://doaj.org/article/8d6ec5fc8fa54345853fc7029f7fdebb kostenfrei https://www.mdpi.com/2227-7390/11/18/3974 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 3974, p 3974
spelling	10.3390/math11183974 doi (DE-627)DOAJ093357834 (DE-599)DOAJ8d6ec5fc8fa54345853fc7029f7fdebb DE-627 ger DE-627 rakwb eng QA1-939 Ying Chen verfasserin aut The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics Xiangyu Pan verfasserin aut Yanyan Xu verfasserin aut Guanggui Chen verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 3974, p 3974 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:3974, p 3974 https://doi.org/10.3390/math11183974 kostenfrei https://doaj.org/article/8d6ec5fc8fa54345853fc7029f7fdebb kostenfrei https://www.mdpi.com/2227-7390/11/18/3974 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 3974, p 3974
allfields_unstemmed	10.3390/math11183974 doi (DE-627)DOAJ093357834 (DE-599)DOAJ8d6ec5fc8fa54345853fc7029f7fdebb DE-627 ger DE-627 rakwb eng QA1-939 Ying Chen verfasserin aut The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics Xiangyu Pan verfasserin aut Yanyan Xu verfasserin aut Guanggui Chen verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 3974, p 3974 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:3974, p 3974 https://doi.org/10.3390/math11183974 kostenfrei https://doaj.org/article/8d6ec5fc8fa54345853fc7029f7fdebb kostenfrei https://www.mdpi.com/2227-7390/11/18/3974 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 3974, p 3974
allfieldsGer	10.3390/math11183974 doi (DE-627)DOAJ093357834 (DE-599)DOAJ8d6ec5fc8fa54345853fc7029f7fdebb DE-627 ger DE-627 rakwb eng QA1-939 Ying Chen verfasserin aut The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics Xiangyu Pan verfasserin aut Yanyan Xu verfasserin aut Guanggui Chen verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 3974, p 3974 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:3974, p 3974 https://doi.org/10.3390/math11183974 kostenfrei https://doaj.org/article/8d6ec5fc8fa54345853fc7029f7fdebb kostenfrei https://www.mdpi.com/2227-7390/11/18/3974 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 3974, p 3974
allfieldsSound	10.3390/math11183974 doi (DE-627)DOAJ093357834 (DE-599)DOAJ8d6ec5fc8fa54345853fc7029f7fdebb DE-627 ger DE-627 rakwb eng QA1-939 Ying Chen verfasserin aut The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics Xiangyu Pan verfasserin aut Yanyan Xu verfasserin aut Guanggui Chen verfasserin aut In Mathematics MDPI AG, 2013 11(2023), 3974, p 3974 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:11 year:2023 number:3974, p 3974 https://doi.org/10.3390/math11183974 kostenfrei https://doaj.org/article/8d6ec5fc8fa54345853fc7029f7fdebb kostenfrei https://www.mdpi.com/2227-7390/11/18/3974 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 3974, p 3974
language	English
source	In Mathematics 11(2023), 3974, p 3974 volume:11 year:2023 number:3974, p 3974
sourceStr	In Mathematics 11(2023), 3974, p 3974 volume:11 year:2023 number:3974, p 3974
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Wiener algebra approximation numbers Kolmogorov numbers entropy numbers Mathematics
isfreeaccess_bool	true
container_title	Mathematics
authorswithroles_txt_mv	Ying Chen @@aut@@ Xiangyu Pan @@aut@@ Yanyan Xu @@aut@@ Guanggui Chen @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	737287764
id	DOAJ093357834
language_de	englisch
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In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi 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callnumber-first	Q - Science
author	Ying Chen
spellingShingle	Ying Chen misc QA1-939 misc Wiener algebra misc approximation numbers misc Kolmogorov numbers misc entropy numbers misc Mathematics The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra
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topic_title	QA1-939 The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra Wiener algebra approximation numbers Kolmogorov numbers entropy numbers
topic	misc QA1-939 misc Wiener algebra misc approximation numbers misc Kolmogorov numbers misc entropy numbers misc Mathematics
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title	The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra
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title_full	The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra
author_sort	Ying Chen
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author_browse	Ying Chen Xiangyu Pan Yanyan Xu Guanggui Chen
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author-letter	Ying Chen
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title_sort	approximation characteristics of weighted <i<p</i<-wiener algebra
callnumber	QA1-939
title_auth	The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra
abstract	In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<.
abstractGer	In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<.
abstract_unstemmed	In this paper, we study the approximation characteristics of weighted <i<p</i<-Wiener algebra <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula< defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<i</mi<<mi<d</mi<<mo<:</mo<<msubsup<<mi mathvariant="script"<A</mi<<mrow<<mi<ω</mi<</mrow<<mi<p</mi<</msubsup<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</semantics<</math<</inline-formula<.
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title_short	The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra
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up_date	2024-07-03T16:50:38.207Z
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mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<<mo<→</mo<<msub<<mi<L</mi<<mi<q</mi<</msub<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< for <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<1</mn<<mo<≤</mo<<mi<p</mi<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<q</mi<<mo<<</mo<<mo<∞</mo<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi mathvariant="script"<A</mi<<mfenced separators="" open="(" close=")"<<msup<<mi mathvariant="double-struck"<T</mi<<mi<d</mi<</msup<</mfenced<</mrow<</semantics<</math<</inline-formula< is the Wiener algebra defined on the <i<d</i<-dimensional torus <inline-formula<<math 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The Approximation Characteristics of Weighted <i<p</i<-Wiener Algebra

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