Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition

Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions...
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Autor*in:	Avdonin, S. A. [verfasserIn] Ivanov, S. A.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Helson–Szegő condition upper uniform density exponential Riesz bases

Anmerkung:	© Pleiades Publishing, Ltd. 2023

Übergeordnetes Werk:	Enthalten in: Mathematical notes - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967, 113(2023), 1-2 vom: Feb., Seite 165-171
Übergeordnetes Werk:	volume:113 ; year:2023 ; number:1-2 ; month:02 ; pages:165-171

Links:	Volltext

DOI / URN:	10.1134/S0001434623010194

Katalog-ID:	SPR049635611

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520			\|a Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class.
650		4	\|a Helson–Szegő condition \|7 (dpeaa)DE-He213
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700	1		\|a Ivanov, S. A. \|4 aut
773	0	8	\|i Enthalten in \|t Mathematical notes \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 \|g 113(2023), 1-2 vom: Feb., Seite 165-171 \|w (DE-627)32557328X \|w (DE-600)2037663-7 \|x 1573-8876 \|7 nnns
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912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
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912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
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912			\|a GBV_ILN_206
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912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
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912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
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
912			\|a GBV_ILN_2049
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912			\|a GBV_ILN_2055
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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
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
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912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
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allfields	10.1134/S0001434623010194 doi (DE-627)SPR049635611 (SPR)S0001434623010194-e DE-627 ger DE-627 rakwb eng Avdonin, S. A. verfasserin aut Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213 Ivanov, S. A. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 1-2 vom: Feb., Seite 165-171 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:1-2 month:02 pages:165-171 https://dx.doi.org/10.1134/S0001434623010194 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_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_206 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_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 113 2023 1-2 02 165-171
spelling	10.1134/S0001434623010194 doi (DE-627)SPR049635611 (SPR)S0001434623010194-e DE-627 ger DE-627 rakwb eng Avdonin, S. A. verfasserin aut Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213 Ivanov, S. A. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 1-2 vom: Feb., Seite 165-171 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:1-2 month:02 pages:165-171 https://dx.doi.org/10.1134/S0001434623010194 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_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_206 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_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 113 2023 1-2 02 165-171
allfields_unstemmed	10.1134/S0001434623010194 doi (DE-627)SPR049635611 (SPR)S0001434623010194-e DE-627 ger DE-627 rakwb eng Avdonin, S. A. verfasserin aut Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213 Ivanov, S. A. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 1-2 vom: Feb., Seite 165-171 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:1-2 month:02 pages:165-171 https://dx.doi.org/10.1134/S0001434623010194 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_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_206 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_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 113 2023 1-2 02 165-171
allfieldsGer	10.1134/S0001434623010194 doi (DE-627)SPR049635611 (SPR)S0001434623010194-e DE-627 ger DE-627 rakwb eng Avdonin, S. A. verfasserin aut Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213 Ivanov, S. A. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 1-2 vom: Feb., Seite 165-171 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:1-2 month:02 pages:165-171 https://dx.doi.org/10.1134/S0001434623010194 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_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_206 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_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 113 2023 1-2 02 165-171
allfieldsSound	10.1134/S0001434623010194 doi (DE-627)SPR049635611 (SPR)S0001434623010194-e DE-627 ger DE-627 rakwb eng Avdonin, S. A. verfasserin aut Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2023 Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213 Ivanov, S. A. aut Enthalten in Mathematical notes Dordrecht [u.a.] : Springer Science + Business Media B.V, 1967 113(2023), 1-2 vom: Feb., Seite 165-171 (DE-627)32557328X (DE-600)2037663-7 1573-8876 nnns volume:113 year:2023 number:1-2 month:02 pages:165-171 https://dx.doi.org/10.1134/S0001434623010194 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_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_206 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_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 113 2023 1-2 02 165-171
language	English
source	Enthalten in Mathematical notes 113(2023), 1-2 vom: Feb., Seite 165-171 volume:113 year:2023 number:1-2 month:02 pages:165-171
sourceStr	Enthalten in Mathematical notes 113(2023), 1-2 vom: Feb., Seite 165-171 volume:113 year:2023 number:1-2 month:02 pages:165-171
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Helson–Szegő condition upper uniform density exponential Riesz bases
isfreeaccess_bool	false
container_title	Mathematical notes
authorswithroles_txt_mv	Avdonin, S. A. @@aut@@ Ivanov, S. A. @@aut@@
publishDateDaySort_date	2023-02-01T00:00:00Z
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author	Avdonin, S. A.
spellingShingle	Avdonin, S. A. misc Helson–Szegő condition misc upper uniform density misc exponential Riesz bases Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition
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topic_title	Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition Helson–Szegő condition (dpeaa)DE-He213 upper uniform density (dpeaa)DE-He213 exponential Riesz bases (dpeaa)DE-He213
topic	misc Helson–Szegő condition misc upper uniform density misc exponential Riesz bases
topic_unstemmed	misc Helson–Szegő condition misc upper uniform density misc exponential Riesz bases
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title	Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition
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title_full	Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition
author_sort	Avdonin, S. A.
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author_browse	Avdonin, S. A. Ivanov, S. A.
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author-letter	Avdonin, S. A.
doi_str_mv	10.1134/S0001434623010194
title_sort	density of zeros of the cartwright class functions and the helson–szegő type condition
title_auth	Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition
abstract	Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. © Pleiades Publishing, Ltd. 2023
abstractGer	Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. © Pleiades Publishing, Ltd. 2023
abstract_unstemmed	Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. Moreover, we show that instead of the last condition one can require that %$\log\|F(x)\|%$ belongs to the BMO class. © Pleiades Publishing, Ltd. 2023
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title_short	Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition
url	https://dx.doi.org/10.1134/S0001434623010194
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author2	Ivanov, S. A.
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doi_str	10.1134/S0001434623010194
up_date	2024-07-04T01:39:28.238Z
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A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Density of Zeros of the Cartwright Class Functions and the Helson–Szegő Type Condition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2023</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract B. Ya. Levin has proved that the zero set of a sine type function can be represented as a union of finitely many separated sets, which is an important result in the theory of exponential Riesz bases. In the present paper, we extend Levin’s result to a more general class of entire functions %$F(z)%$ with zeros in a strip %$\sup\|{\operatorname{Im}\lambda_n}\|<\infty%$ such that %$\|F(x)\|^2%$ satisfies the Helson–Szegő condition. 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