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 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| 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| _version_ | 1862597805743276032 |
|---|---|
| author | Cardoso, J.L. |
| author_facet | Cardoso, J.L. |
| citation_txt | On Basic Fourier-Bessel Expansions / J.L. Cardoso // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T12:29:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209537 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T12:29:55Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | On Basic Fourier-Bessel Expansions Cardoso, J.L. |
| title | 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_short | On Basic Fourier-Bessel Expansions |
| title_sort | on basic fourier-bessel expansions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209537 |
| work_keys_str_mv | AT cardosojl onbasicfourierbesselexpansions |