Equivalence of \(K\)-functionals and modulus of smoothness constructed by Cherednik-Opdam transform

zbMath1487.42057MaRDI QIDQ2135508

Mohamed El Hamma, Radouan Daher, N. Djellab

Publication date: 9 May 2022

Published in: Nihonkai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/nihonkai-mathematical-journal/volume-32/issue-2/Equivalence-of-K-Functionals-and-Modulus-of-Smoothness-Constructed-by/nihmj/1644406454.full

zbMATH Keywords

\(K\)-functionalmodulus of smoothnessgeneralized translation operator

Mathematics Subject Classification ID

Harmonic analysis and PDEs (42B37)

Cites Work

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• Some new estimates for the Cherednik-Opdam transform in the space \(L^{2}_{\alpha ,\beta}(\mathbb {R})\)
• Equivalence of \(K\)-functionals and modulus of smoothness constructed by generalized Dunkl translations
• Growth properties of Fourier transforms via moduli of continuity
• Harmonic analysis for certain representations of graded Hecke algebras
• Estimate of \(K\)-functionals and modulus of smoothness constructed by generalized spherical mean operator
• Moduli of smoothness and \(K\)-functional in \(L_2(\mathbb{R}_q^+)\)-space with power weight
• Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
• Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Jackson's type direct theorems
• Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform

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