Paley-Wiener theorem for the \(q\)-Bessel transform and associated \(q\)-sampling formula

DOI10.1016/j.exmath.2008.07.002zbMath1172.33308OpenAlexW1963657087MaRDI QIDQ1004605

Ahmed Fitouhi, Wafa Binous, Lazhar Dhaouadi

Publication date: 11 March 2009

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2008.07.002

zbMATH Keywords

Paley-Wiener theoremq-Bessel transformq-sampling formula

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic hypergeometric integrals and functions defined by them (33D60) Applications of basic hypergeometric functions (33D90)

Related Items (13)

Variations around a general quantum operator ⋮ Bessel-Wright transform in the setting of quantum calculus ⋮ \(q\)-Macdonald function as a variation diminishing \({^\ast}_q\)-kernel ⋮ Windowed Bessel Fourier transform in quantum calculus and applications ⋮ Uncertainty principles for the \(q\)-Bessel windowed transform and localization operators ⋮ \(q\)-Bessel positive definite and \(D _{q }\)-completely monotonic functions ⋮ Aβ-Sturm–Liouville problem associated with the general quantum operator ⋮ An analog of Titchmarsh's theorem for the \(q\)-Bessel transform ⋮ Sampling theorems associated with singular \(q\)-Sturm Liouville problems ⋮ Calderón's reproducing formula and uncertainty principle for the continuous wavelet transform associated with the \(q\)-Bessel operator ⋮ On \(q\)-Bessel Fourier analysis method for classical moment problem ⋮ Unnamed Item ⋮ Localization operators associated with the q-Bessel wavelet transform and applications

Cites Work

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• On a \(q\)-Paley--Wiener theorem
• \(q\)-prolate spheroidal wave functions and \(q\)-sampling theorem
• On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
• The \textit{q-j}\(_\alpha\) Bessel function
• A \(q\)-analogue of Graf's addition formula for the Hahn-Exton \(q\)-Bessel function
• On sampling theory and basic Sturm-Liouville systems
• A 𝑞-sampling theorem related to the 𝑞-Hankel transform
• On q-Analogues of the Fourier and Hankel Transforms
• An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
• A q-Analogue of the Wronskian and a Second Solution of the Hahn-Exton q-Bessel Difference Equation
• A 𝑞-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem

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