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 |
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| 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| Summary: | 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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| ISSN: | 1815-0659 |