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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Bibliographic Details
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
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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.
ISSN:1815-0659