On spherical analogues of the classical theorems of Titchmarsh

DOI10.1080/10652469.2020.1784162zbMath1476.43003OpenAlexW3081280616MaRDI QIDQ4987930

Radouan Daher, Salah El Ouadih

Publication date: 11 May 2021

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2020.1784162

zbMATH Keywords

spherical harmonicLipschitz conditionGegenbauer polynomialspherical shift

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)

Related Items

Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series ⋮ Discrete Fourier-Laplace transforms of Lipschitz functions in the spaces \(S^{(p,q)}(\sigma^{m-1})\)

Cites Work

• An analog of Titchmarsh's theorem for the generalized Dunkl transform
• Characterization of Dini-Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces
• Fourier transforms of Dini-Lipschitz functions on rank 1 symmetric spaces
• Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on \([0, \pi\)]
• An analog of Titchmarsh's theorem for the generalized Fourier-Bessel transform
• Fourier transforms of Dini-Lipschitz functions
• Fourier-Bessel Dini Lipschitz functions in the space \(L_{\alpha,n}^{2}\)
• Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds
• Dini Lipschitz functions for the Dunkl transform in the space \(\mathrm{L}^{2}(\mathbb{R}^{d},w_{k}(x)dx)\)
• Some problems in the theory of approximation of functions on compact homogeneous manifolds
• Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
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