An analog of Titchmarsh's theorem for the q-Dunkl transform in the space \(L_{q,\alpha }^2({\mathbb{R}}_q)\)

DOI10.1007/s11868-020-00330-6zbMath1475.33008OpenAlexW3004163888MaRDI QIDQ2210494

Othman Tyr, Radouan Daher

Publication date: 6 November 2020

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-020-00330-6

zbMATH Keywords

\(q\)-Titchmarsh's theoremgeneralized \(q\)-Dunkl translation\(q\)-Dunkl tansform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Inequalities involving derivatives and differential and integral operators (26D10)

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Cites Work

• Unnamed Item
• A \(q^ 2\)-analogue operator for \(q^ 2\)-analogue Fourier analysis
• Moduli of smoothness and \(K\)-functional in \(L_2(\mathbb{R}_q^+)\)-space with power weight
• Duhamel solutions of non-homogeneous $q^2$-analogue wave equations
• $q$-Analogue of the Dunkl transform on the real line