Harmonic analysis associated with the Jacobi-Dunkl operator on \(]-\frac{\pi}{2},\frac{\pi}{2}[\)

DOI10.1016/j.cam.2004.02.025zbMath1062.43011OpenAlexW1511432181MaRDI QIDQ1772332

Frej Chouchene

Publication date: 18 April 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.02.025

zbMATH Keywords

Harmonic analysisJacobi-Dunkl operatorLaplace integral representations

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Other transforms and operators of Fourier type (43A32)

Related Items (15)

Generalized distributions and Jacobi-Dunkl approximations ⋮ A new aspect of generalized integral operator and an estimation in a generalized function theory ⋮ de La Vallée Poussin approximations and Jacobi-Dunkl convolution structures ⋮ Discrete Jacobi-Dunkl transform and approximation theorems ⋮ Spectral properties of differential-difference symmetrized operators ⋮ On the approximation of functions by Jacobi-Dunkl expansions in the weighted space \({\mathbb{L}}_2^{\left(\alpha ,\beta \right)} \) ⋮ Harmonic analysis associated with the Jacobi-Dunkl operator on \((-\pi, \pi)\): exotic cases ⋮ Some direct and inverse theorems of approximation of functions in Jacobi-Dunkl discrete harmonic analysis ⋮ Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ The finite continuous nonsymmetric Jacobi transform and applications ⋮ Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials ⋮ Discrete diffusion semigroups associated with Jacobi-Dunkl and exceptional Jacobi polynomials ⋮ Herglotz's theorem for Jacobi-Dunkl positive definite sequences ⋮ Dirichlet Theorem for Jacobi-Dunkl Expansions ⋮ Superstatistics of the Dunkl oscillator

Cites Work

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• Differential-Difference Operators Associated to Reflection Groups
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• Multiplier Criteria of Marcinkiewicz Type for Jacobi Expansions
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$

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