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Irregular sampling for hyperbolic secant type functions. / Baranov, A.; Belov, Y.

в: Advances in Mathematics, Том 458, № Part B, 109981, 01.12.2024.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Baranov, A & Belov, Y 2024, 'Irregular sampling for hyperbolic secant type functions', Advances in Mathematics, Том. 458, № Part B, 109981. https://doi.org/10.1016/j.aim.2024.109981

APA

Baranov, A., & Belov, Y. (2024). Irregular sampling for hyperbolic secant type functions. Advances in Mathematics, 458(Part B), [109981]. https://doi.org/10.1016/j.aim.2024.109981

Vancouver

Baranov A, Belov Y. Irregular sampling for hyperbolic secant type functions. Advances in Mathematics. 2024 Дек. 1;458(Part B). 109981. https://doi.org/10.1016/j.aim.2024.109981

Author

Baranov, A. ; Belov, Y. / Irregular sampling for hyperbolic secant type functions. в: Advances in Mathematics. 2024 ; Том 458, № Part B.

BibTeX

@article{4c5082741dc54c5b861df1dcc5468658,
title = "Irregular sampling for hyperbolic secant type functions",
abstract = "We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., g(x)=(eax+e−bx)−1, Rea,Reb>0. A criterion for half-regular sampling is obtained: for a separated Λ⊂R the Gabor system G(g,Λ×αZ) is a frame in L2(R) if and only if D−(Λ)>α where D−(Λ) is the usual (Beurling) lower density of Λ. This extends a result by Gr{\"o}chenig, Romero, and St{\"o}ckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by g is given. {\textcopyright} 2024 Elsevier Inc.",
keywords = "Gabor systems, Sampling, Shift-invariant space, Small Fock spaces",
author = "A. Baranov and Y. Belov",
note = "Export Date: 10 November 2024 Сведения о финансировании: Russian Science Foundation, RSF, 19-71-30002 Сведения о финансировании: Russian Science Foundation, RSF Текст о финансировании 1: The work is supported by Russian Science Foundation project 19-71-30002.Acknowledgments. The authors are grateful to Karlheinz Gr\u00F6chenig for numerous helpful comments and to the anonymous referee for the careful reading of the paper and many useful remarks and suggestions. The second author is a winner of the \u201CLeader\u201D contest conducted by the Foundation for the Advancement of Theoretical Physics and Mathematics \u201CBASIS\u201D and would like to thank its sponsors and jury.",
year = "2024",
month = dec,
day = "1",
doi = "10.1016/j.aim.2024.109981",
language = "Английский",
volume = "458",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Elsevier",
number = "Part B",

}

RIS

TY - JOUR

T1 - Irregular sampling for hyperbolic secant type functions

AU - Baranov, A.

AU - Belov, Y.

N1 - Export Date: 10 November 2024 Сведения о финансировании: Russian Science Foundation, RSF, 19-71-30002 Сведения о финансировании: Russian Science Foundation, RSF Текст о финансировании 1: The work is supported by Russian Science Foundation project 19-71-30002.Acknowledgments. The authors are grateful to Karlheinz Gr\u00F6chenig for numerous helpful comments and to the anonymous referee for the careful reading of the paper and many useful remarks and suggestions. The second author is a winner of the \u201CLeader\u201D contest conducted by the Foundation for the Advancement of Theoretical Physics and Mathematics \u201CBASIS\u201D and would like to thank its sponsors and jury.

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., g(x)=(eax+e−bx)−1, Rea,Reb>0. A criterion for half-regular sampling is obtained: for a separated Λ⊂R the Gabor system G(g,Λ×αZ) is a frame in L2(R) if and only if D−(Λ)>α where D−(Λ) is the usual (Beurling) lower density of Λ. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by g is given. © 2024 Elsevier Inc.

AB - We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., g(x)=(eax+e−bx)−1, Rea,Reb>0. A criterion for half-regular sampling is obtained: for a separated Λ⊂R the Gabor system G(g,Λ×αZ) is a frame in L2(R) if and only if D−(Λ)>α where D−(Λ) is the usual (Beurling) lower density of Λ. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by g is given. © 2024 Elsevier Inc.

KW - Gabor systems

KW - Sampling

KW - Shift-invariant space

KW - Small Fock spaces

UR - https://www.mendeley.com/catalogue/0ff7c2ce-5cce-3910-84f5-87322778ae24/

U2 - 10.1016/j.aim.2024.109981

DO - 10.1016/j.aim.2024.109981

M3 - статья

VL - 458

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - Part B

M1 - 109981

ER -

ID: 127101662