Dunkl's theory and Jackson's theorem in the space \(L_2(\mathbb R^d)\) with power weight

DOI10.1134/S0081543811050099zbMath1229.42022OpenAlexW2070595362MaRDI QIDQ643838

Valeriĭ I. Ivanov, Alexey Ivanov

Publication date: 2 November 2011

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543811050099

zbMATH Keywords

modulus of continuityJackson inequalitybest approximationreflection groupDunkl transform

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Harmonic analysis and almost periodicity in probabilistic number theory (11K70)

Related Items (4)

Boundedness of bilinear Dunkl–Hausdorff operators on products of Lebesgue and Morrey spaces ⋮ Dunkl's theory and best approximation by entire functions of exponential type in \(L_{2}\)-metric with power weight ⋮ An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin \(L_2\)-inequality ⋮ Generalized Jackson inequality in the space \(L_2(\mathbb{R}^{d})\) with Dunkl weight

Cites Work

• Unnamed Item
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Reflection groups and orthogonal polynomials on the sphere
• Positivity of Dunkl's intertwining operator
• Convolution operator and maximal function for the Dunkl transform
• Integral Kernels with Reflection Group Invariance
• Funk-Hecke Formula for Orthogonal Polynomials on Spheres and on Balls
• A positive radial product formula for the Dunkl kernel
• Paley–Wiener theorems for the Dunkl transform

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