Herglotz's theorem for Jacobi-Dunkl positive definite sequences

DOI10.1515/MS-2021-0011zbMath1493.43002OpenAlexW3176852698MaRDI QIDQ2054659

Frej Chouchene, Iness Haouala

Publication date: 3 December 2021

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ms-2021-0011

zbMATH Keywords

Herglotz's theoremJacobi-Dunkl polynomialsdiscrete Jacobi-Dunkl convolutiondiscrete Jacobi-Dunkl translation operatorsJacobi-Dunkl positive definite sequences

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Positive definite functions in one variable harmonic analysis (42A82) Other special orthogonal polynomials and functions (33C47) Positive definite functions on groups, semigroups, etc. (43A35) Exponential and trigonometric functions (33B10)

Related Items (1)

Fractional Jacobi-Dunkl transform: properties and application

Cites Work

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• The Riesz representation theorem
• Characterizations of smoothness of functions in terms of the basis conjugate to Jacobi polynomials
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• Uncertainty principles for Jacobi expansions
• Harmonic analysis associated with the Jacobi-Dunkl operator on \(-\frac{\pi}{2},\frac{\pi}{2}[\)]
• Trigonometric convolution structures on \(\mathbb{Z}\) derived from Jacobi polynomials
• Conjugate Jacobi series and conjugate functions
• Hardy spaces for Dunkl-Gegenbauer expansions
• HARDY SPACES FOR JACOBI EXPANSIONS I. THE BASIC THEORY
• Functional Analysis, Spectral Theory, and Applications

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