Dunkl's theory and best approximation by entire functions of exponential type in \(L_{2}\)-metric with power weight

DOI10.1007/S10114-014-2415-1zbMath1304.41020OpenAlexW2079570611MaRDI QIDQ477852

Chun Yuan Song, Yong-ping Liu

Publication date: 10 December 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-014-2415-1

zbMATH Keywords

Jackson inequalityBessel functionreflection groupDunkl transformcontinuous modulus

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Cites Work

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• The Jackson inequality and widths of function classes in \(L^2([0,1,x^{2v+1})\)]
• Dunkl's theory and Jackson's theorem in the space \(L_2(\mathbb R^d)\) with power weight
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Sharp Jackson-Stechkin inequality in \(L^2\) for multidimensional spheres
• Two related extremal problems for entire functions of several variables
• Jackson inequalities on sphere in \(L_ 2\)
• Positivity of Dunkl's intertwining operator
• The sharp Jackson inequality in the space \(L_{2}\) on the segment \([-1, 1\) with the power weight]
• Convolution operator and maximal function for the Dunkl transform
• Higher monotonicity properties of normalized Bessel functions
• Integral Kernels with Reflection Group Invariance
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• Paley–Wiener theorems for the Dunkl transform

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