Positivity of the generalized translation associated with theq-Hankel transform and applications

DOI10.1080/10652469.2014.973192zbMath1311.47037OpenAlexW1994247857MaRDI QIDQ5498532

Lazhar Dhaouadi

Publication date: 9 February 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2014.973192

zbMATH Keywords

Markov operators\(q\)-Lommel polynomials\(q\)-Bessel Fourier transform\(q\)-Bessel positive and negative definitepositivity of the generalized translation

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Integral transforms of special functions (44A20) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (3)

Bilateral birth and death process in q-calculus ⋮ An analog of Titchmarsh's theorem for the \(q\)-Bessel transform ⋮ Uncertainty principles for the q-bessel fourier transform

Cites Work

• \(q\)-Bessel positive definite and \(D _{q }\)-completely monotonic functions
• Positivity of the generalized translation associated with the \(q\)-Hankel transform
• On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
• The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function
• The \textit{q-j}\(_\alpha\) Bessel function
• A \(q\)-analogue of Graf's addition formula for the Hahn-Exton \(q\)-Bessel function
• Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton \(q\)-Bessel function
• On the Lévy-Khintchine representation of \(q\)-Bessel negative definite functions
• Elements of harmonic analysis related to the third basic zero order Bessel function
• On q-Analogues of the Fourier and Hankel Transforms

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