The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle

Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heise...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	El Haoui, Youssef [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Quaternion algebra Quaternion Fourier transform Admissible quaternion wavelet Uncertainty principle

Übergeordnetes Werk:	Enthalten in: Journal of pseudo-differential operators and applications - Cham (ZG) : Springer International Publishing AG, 2010, 12(2021), 1 vom: 18. Feb.
Übergeordnetes Werk:	volume:12 ; year:2021 ; number:1 ; day:18 ; month:02

Links:	Volltext

DOI / URN:	10.1007/s11868-021-00396-w

Katalog-ID:	SPR043232108

Internformat


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520			\|a Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain.
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650		4	\|a Quaternion Fourier transform \|7 (dpeaa)DE-He213
650		4	\|a Admissible quaternion wavelet \|7 (dpeaa)DE-He213
650		4	\|a Uncertainty principle \|7 (dpeaa)DE-He213
773	0	8	\|i Enthalten in \|t Journal of pseudo-differential operators and applications \|d Cham (ZG) : Springer International Publishing AG, 2010 \|g 12(2021), 1 vom: 18. Feb. \|w (DE-627)623181061 \|w (DE-600)2546244-1 \|x 1662-999X \|7 nnns
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912			\|a GBV_ILN_602
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912			\|a GBV_ILN_2025
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912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
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912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
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912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
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publishDate	2021
allfields	10.1007/s11868-021-00396-w doi (DE-627)SPR043232108 (DE-599)SPRs11868-021-00396-w-e (SPR)s11868-021-00396-w-e DE-627 ger DE-627 rakwb eng 510 ASE El Haoui, Youssef verfasserin aut The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain. Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213 Enthalten in Journal of pseudo-differential operators and applications Cham (ZG) : Springer International Publishing AG, 2010 12(2021), 1 vom: 18. Feb. (DE-627)623181061 (DE-600)2546244-1 1662-999X nnns volume:12 year:2021 number:1 day:18 month:02 https://dx.doi.org/10.1007/s11868-021-00396-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2021 1 18 02
spelling	10.1007/s11868-021-00396-w doi (DE-627)SPR043232108 (DE-599)SPRs11868-021-00396-w-e (SPR)s11868-021-00396-w-e DE-627 ger DE-627 rakwb eng 510 ASE El Haoui, Youssef verfasserin aut The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain. Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213 Enthalten in Journal of pseudo-differential operators and applications Cham (ZG) : Springer International Publishing AG, 2010 12(2021), 1 vom: 18. Feb. (DE-627)623181061 (DE-600)2546244-1 1662-999X nnns volume:12 year:2021 number:1 day:18 month:02 https://dx.doi.org/10.1007/s11868-021-00396-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2021 1 18 02
allfields_unstemmed	10.1007/s11868-021-00396-w doi (DE-627)SPR043232108 (DE-599)SPRs11868-021-00396-w-e (SPR)s11868-021-00396-w-e DE-627 ger DE-627 rakwb eng 510 ASE El Haoui, Youssef verfasserin aut The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain. Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213 Enthalten in Journal of pseudo-differential operators and applications Cham (ZG) : Springer International Publishing AG, 2010 12(2021), 1 vom: 18. Feb. (DE-627)623181061 (DE-600)2546244-1 1662-999X nnns volume:12 year:2021 number:1 day:18 month:02 https://dx.doi.org/10.1007/s11868-021-00396-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2021 1 18 02
allfieldsGer	10.1007/s11868-021-00396-w doi (DE-627)SPR043232108 (DE-599)SPRs11868-021-00396-w-e (SPR)s11868-021-00396-w-e DE-627 ger DE-627 rakwb eng 510 ASE El Haoui, Youssef verfasserin aut The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain. Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213 Enthalten in Journal of pseudo-differential operators and applications Cham (ZG) : Springer International Publishing AG, 2010 12(2021), 1 vom: 18. Feb. (DE-627)623181061 (DE-600)2546244-1 1662-999X nnns volume:12 year:2021 number:1 day:18 month:02 https://dx.doi.org/10.1007/s11868-021-00396-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2021 1 18 02
allfieldsSound	10.1007/s11868-021-00396-w doi (DE-627)SPR043232108 (DE-599)SPRs11868-021-00396-w-e (SPR)s11868-021-00396-w-e DE-627 ger DE-627 rakwb eng 510 ASE El Haoui, Youssef verfasserin aut The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain. Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213 Enthalten in Journal of pseudo-differential operators and applications Cham (ZG) : Springer International Publishing AG, 2010 12(2021), 1 vom: 18. Feb. (DE-627)623181061 (DE-600)2546244-1 1662-999X nnns volume:12 year:2021 number:1 day:18 month:02 https://dx.doi.org/10.1007/s11868-021-00396-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2021 1 18 02
language	English
source	Enthalten in Journal of pseudo-differential operators and applications 12(2021), 1 vom: 18. Feb. volume:12 year:2021 number:1 day:18 month:02
sourceStr	Enthalten in Journal of pseudo-differential operators and applications 12(2021), 1 vom: 18. Feb. volume:12 year:2021 number:1 day:18 month:02
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Quaternion algebra Quaternion Fourier transform Admissible quaternion wavelet Uncertainty principle
dewey-raw	510
isfreeaccess_bool	false
container_title	Journal of pseudo-differential operators and applications
authorswithroles_txt_mv	El Haoui, Youssef @@aut@@
publishDateDaySort_date	2021-02-18T00:00:00Z
hierarchy_top_id	623181061
dewey-sort	3510
id	SPR043232108
language_de	englisch
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author	El Haoui, Youssef
spellingShingle	El Haoui, Youssef ddc 510 misc Quaternion algebra misc Quaternion Fourier transform misc Admissible quaternion wavelet misc Uncertainty principle The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
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topic_title	510 ASE The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle Quaternion algebra (dpeaa)DE-He213 Quaternion Fourier transform (dpeaa)DE-He213 Admissible quaternion wavelet (dpeaa)DE-He213 Uncertainty principle (dpeaa)DE-He213
topic	ddc 510 misc Quaternion algebra misc Quaternion Fourier transform misc Admissible quaternion wavelet misc Uncertainty principle
topic_unstemmed	ddc 510 misc Quaternion algebra misc Quaternion Fourier transform misc Admissible quaternion wavelet misc Uncertainty principle
topic_browse	ddc 510 misc Quaternion algebra misc Quaternion Fourier transform misc Admissible quaternion wavelet misc Uncertainty principle
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title	The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
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title_full	The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
author_sort	El Haoui, Youssef
journal	Journal of pseudo-differential operators and applications
journalStr	Journal of pseudo-differential operators and applications
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title_sort	continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
title_auth	The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
abstract	Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain.
abstractGer	Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain.
abstract_unstemmed	Abstract This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP to the CQWT domain.
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title_short	The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle
url	https://dx.doi.org/10.1007/s11868-021-00396-w
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doi_str	10.1007/s11868-021-00396-w
up_date	2024-07-03T17:23:57.804Z
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We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity, then we derive the associated Heisenberg–Pauli–Weyl uncertainty principle UP. 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The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle

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