The multiplier of the interval \([-1,1]\) for the Dunkl transform on the real line

DOI10.1016/J.JFA.2006.04.002zbMath1109.44002OpenAlexW2018959833MaRDI QIDQ859652

Óscar Ciaurri, Juan Luis Varona, Jorge J. Betancor

Publication date: 16 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.04.002

zbMATH Keywords

Hankel transformBessel functionsDunkl operatorDunkl transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (16)

The spectrum of the right inverse of the Dunkl operator ⋮ A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform ⋮ Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions ⋮ Linear and bilinear multiplier operators for the Dunkl transform ⋮ Boole-Dunkl polynomials and generalizations ⋮ Interpolation by weighted Paley-Wiener spaces associated with the Dunkl transform ⋮ Harmonic analysis associated with the one-dimensional Dunkl transform ⋮ Relating transplantation and multipliers for Dunkl and Hankel transforms ⋮ Unnamed Item ⋮ \(L^p\) estimates for an oscillating Dunkl multiplier ⋮ Mean convergence of Fourier-Dunkl series ⋮ Calderón’s reproducing formulas for the Weinstein L2-multiplier operators ⋮ Bilinear biorthogonal expansions and the Dunkl kernel on the real line ⋮ Unnamed Item ⋮ On the Dunkl convolution equations in spaces of type ⋮ The multiplier of the interval [−1, 1 for the Dunkl transform of arbitrary order on the real line]

Cites Work

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• The Dunkl transform
• Fourier series of functions whose Hankel transform is supported on \([0,1\)]
• \(L^{p}\)-Fourier multipliers for the Dunkl operator on the real line.
• A note on \(A_p\) weights: Pasting weights and changing variables.
• Transplanting maximal inequalities between Laguerre and Hankel multipliers
• Solving dual integral equations on Lebesgue spaces
• Differential-Difference Operators Associated to Reflection Groups
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
• ON THE MEAN INVERSION OF FOURIER AND HANKEL TRANSFORMS

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