On Basic Fourier-Bessel Expansions

When dealing with Fourier expansions using the third Jackson (also known as Hahn-Exton) q-Bessel function, the corresponding positive zeros jkν and the "shifted" zeros, qjkν, among others, play an essential role. Mixing classical analysis with q-analysis, we were able to prove asymptotic r...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Cardoso, J.L.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209537
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On Basic Fourier-Bessel Expansions / J.L. Cardoso // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209537
record_format dspace
spelling Cardoso, J.L.
2025-11-24T10:46:11Z
2018
On Basic Fourier-Bessel Expansions / J.L. Cardoso // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 42C10; 33D45; 33D15
arXiv: 1707.05216
https://nasplib.isofts.kiev.ua/handle/123456789/209537
https://doi.org/10.3842/SIGMA.2018.035
When dealing with Fourier expansions using the third Jackson (also known as Hahn-Exton) q-Bessel function, the corresponding positive zeros jkν and the "shifted" zeros, qjkν, among others, play an essential role. Mixing classical analysis with q-analysis, we were able to prove asymptotic relations between those zeros and the "shifted" ones, as well as the asymptotic behavior of the third Jackson q-Bessel function when computed on the ''shifted'' zeros. A version of a q-analogue of the Riemann-Lebesgue theorem within the scope of basic Fourier-Bessel expansions is also exhibited.
The author wants to thank the unknown referees for the valuable comments and remarks that helped to improve the paper. The author is also grateful to Professor José Carlos Petronilho from CMUC (University of Coimbra) and Professor Renato Álvarez-Nodarse (University of Seville) for the valuable discussions. This research was partially supported by FCT - Fundação para a Ciência e a Tecnologia, within the project UID-MAT-00013/2013.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Basic Fourier-Bessel Expansions
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Basic Fourier-Bessel Expansions
spellingShingle On Basic Fourier-Bessel Expansions
Cardoso, J.L.
title_short On Basic Fourier-Bessel Expansions
title_full On Basic Fourier-Bessel Expansions
title_fullStr On Basic Fourier-Bessel Expansions
title_full_unstemmed On Basic Fourier-Bessel Expansions
title_sort on basic fourier-bessel expansions
author Cardoso, J.L.
author_facet Cardoso, J.L.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description When dealing with Fourier expansions using the third Jackson (also known as Hahn-Exton) q-Bessel function, the corresponding positive zeros jkν and the "shifted" zeros, qjkν, among others, play an essential role. Mixing classical analysis with q-analysis, we were able to prove asymptotic relations between those zeros and the "shifted" ones, as well as the asymptotic behavior of the third Jackson q-Bessel function when computed on the ''shifted'' zeros. A version of a q-analogue of the Riemann-Lebesgue theorem within the scope of basic Fourier-Bessel expansions is also exhibited.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209537
citation_txt On Basic Fourier-Bessel Expansions / J.L. Cardoso // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.
work_keys_str_mv AT cardosojl onbasicfourierbesselexpansions
first_indexed 2025-12-07T12:29:55Z
last_indexed 2025-12-07T12:29:55Z
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