Sonine-type integral transforms related to the Dunkl operator on the real line

DOI10.1080/10652460903024251zbMath1232.44004OpenAlexW2070623895MaRDI QIDQ3651173

Mohamed Ali Mourou

Publication date: 8 December 2009

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

Full work available at URL: https://doi.org/10.1080/10652460903024251

zbMATH Keywords

differential-difference operatorDunkl kerneldual Sonine-Dunkl integral transformSonine-Dunkl integral transformSonine-type integral representation

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Other special orthogonal polynomials and functions (33C47) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (3)

Sharp Bernstein inequalities for Jacobi-Dunkl operators ⋮ Fractional Riesz–Feller type derivative for the one dimensional Dunkl operator and Lipschitz condition ⋮ Generalized Sonine-type integral transforms on the real line

Cites Work

• Unnamed Item
• Calderon's reproducing formula related to the Dunkl operator on the real line
• Integral Kernels with Reflection Group Invariance
• Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A Note on the Quantum Rule of the Harmonic Oscillator

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