Equivalence of \(K\)-functionals and modulus of smoothness generated by a Dunkl type operator on the interval \((-1, 1)\)

DOI10.5802/crmath.517MaRDI QIDQ6122542

Faouaz Saadi, Radouan Daher

Publication date: 1 March 2024

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

modulus of smoothness\(K\)-functionalsgeneralized translation operatorDunkl transformFourier-Dunkl series

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Basic hypergeometric integrals and functions defined by them (33D60)

Cites Work

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• Equivalence of \(K\)-functionals and modulus of smoothness constructed by generalized Dunkl translations
• Riesz transform and Riesz potentials for Dunkl transform
• Mean convergence of Fourier-Dunkl series
• An uncertainty inequality for Fourier-Dunkl series
• Sugli zeri delle funzioni di Bessel
• The Dunkl transform
• Harmonic analysis associated with the one-dimensional Dunkl transform
• Appell-Dunkl sequences and Hurwitz-Dunkl zeta functions
• A differential equation for the zeros of bessel functions
• Integral Kernels with Reflection Group Invariance
• A positive radial product formula for the Dunkl kernel
• A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform
• Bessel harmonic analysis and approximation of functions on the half-line

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