Dini Lipschitz functions for the Dunkl transform in the space \(\mathrm{L}^{2}(\mathbb{R}^{d},w_{k}(x)dx)\)

DOI10.1007/s12215-015-0195-9zbMath1320.42007OpenAlexW1763694799WikidataQ59430131 ScholiaQ59430131MaRDI QIDQ2515999

Radouan Daher, Mohamed El Hamma

Publication date: 7 August 2015

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-015-0195-9

zbMATH Keywords

Dunkl kernelDunkl transformgeneralized spherical mean operatorDini Lipschitz functions

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis and PDEs (42B37)

Related Items (9)

Best trigonometric approximation and Dini-Lipschitz classes ⋮ Lipschitz conditions in Laguerre hypergroup ⋮ Titchmarsh's theorems, \(K\)-functional and Jackson's theorems for the free metaplectic transform ⋮ Lipschitz conditions in Damek-Ricci spaces ⋮ Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on \([0, \pi\)] ⋮ Discrete Fourier-Laplace transforms of Lipschitz functions in the spaces \(S^{(p,q)}(\sigma^{m-1})\) ⋮ Modulus of continuity and modulus of smoothness related to the deformed Hankel transform ⋮ On spherical analogues of the classical theorems of Titchmarsh ⋮ On the generalized Dunkl Dini–Lipschitz spaces

Cites Work

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• Bessel transform of \((k, \gamma)\)-Bessel Lipschitz functions
• Fourier transforms of Dini-Lipschitz functions
• Markov processes related with Dunkl operators
• The Dunkl transform
• Approximation of functions by the Fourier-Bessel sums
• Convolution operator and maximal function for the Dunkl transform
• Some remarks concerning the Fourier transform in the space L 2 (ℝ)
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators

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