An analog of Titchmarsh's theorem for the \(q\)-Bessel transform

DOI10.1007/s11565-018-0309-3zbMath1415.33006OpenAlexW2895433631WikidataQ129150781 ScholiaQ129150781MaRDI QIDQ2000591

EL. Loualid, Azzedine Achak, Radouan Daher, Lazhar Dhaouadi

Publication date: 28 June 2019

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-018-0309-3

zbMATH Keywords

\(K\)-functional\(q\)-Bessel transform\(q\)-Bessel operator\(q\)-Titchmarsh's theorem

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (6)

Boas and Titchmarsh type theorems for generalized Lipschitz classes and \(q\)-Bessel Fourier transform ⋮ Titchmarsh's theorem and some remarks concerning the right-sided quaternion Fourier transform ⋮ Discrete Fourier-Jacobi transform and generalized Lipschitz classes ⋮ Deformed Hankel transform of Dini-Lipschitz functions ⋮ Generalization of Titchmarsh theorem in the deformed Hankel setting ⋮ Boas-type theorems for the \(q\)-Bessel Fourier transform

Cites Work

• Positivity of the generalized translation associated with the \(q\)-Hankel transform
• Paley-Wiener theorem for the \(q\)-Bessel transform and associated \(q\)-sampling formula
• Some equivalence theorems with \(K\)-functionals
• Approximation theorems connected with generalized translations
• On q-Analogues of the Fourier and Hankel Transforms
• An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
• On the $q$-Bessel Fourier transform
• Positivity of the generalized translation associated with theq-Hankel transform and applications
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