Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on [0,<i>π</i>]

Salah El Ouadih; Radouan Daher

doi:10.1016/j.crma.2017.01.017

Harmonic analysis

Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on [0,π]
[Conditions de Lipschitz pour la transformée de Fourier discrète généralisée associée à l'opérateur de Jacobi sur [0,π]]

Présenté par : the Editorial Board

Salah El Ouadih ¹ ; Radouan Daher ¹

¹ Department of Mathematics, Faculty of Sciences Aïn Chock, University Hassan II, Casablanca, Morocco

Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 318-324.

Résumé
Abstract

L'objectif de cette Note est de prouver un analogue du théorème de Titchmarsh sur l'image sous la transformée de Fourier–Jacobi discrète d'un jeu de fonctions satisfaisant une condition de Lipschitz généralisée dans l'espace $L_{2}^{(α, β)}$ .

Our aim in this paper is to prove an analog of the classical Titchmarsh theorem on the image under the discrete Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition in the space $L_{2}^{(α, β)}$ .

Reçu le : 2016-08-04
Accepté le : 2017-01-23
Publié le : 2017-02-20

DOI : 10.1016/j.crma.2017.01.017

Affiliations des auteurs :

Salah El Ouadih ¹ ; Radouan Daher ¹

¹ Department of Mathematics, Faculty of Sciences Aïn Chock, University Hassan II, Casablanca, Morocco

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Salah El Ouadih; Radouan Daher. Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on [0,π]. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 318-324. doi : 10.1016/j.crma.2017.01.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.017/

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Othman Tyr; Radouan Daher Generalized Lipschitz conditions for absolute convergence of weighted Jacobi–Dunkl series, Boletín de la Sociedad Matemática Mexicana, Volume 30 (2024) no. 1 | DOI:10.1007/s40590-023-00581-5
Othman Tyr On the Fourier–Dunkl Coefficients of Generalized Lipschitz Classes on the Interval $[- 1, 1]$ , Mediterranean Journal of Mathematics, Volume 21 (2024) no. 5 | DOI:10.1007/s00009-024-02710-4
Salah El Ouadih; Radouan Daher Generalized Lipschitz and Besov spaces in terms of decay of Dunkl transforms in the space $L^{2} (R^{d}, w_{l} (x) d x)$ , Rendiconti del Circolo Matematico di Palermo Series 2, Volume 73 (2024) no. 8, p. 2955 | DOI:10.1007/s12215-024-01086-4
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S. El Ouadih Discrete Fourier–Laplace Transforms of Lipschitz Functions in the Spaces $S^{(p, q)} (σ^{m - 1})$ , Complex Analysis and Operator Theory, Volume 15 (2021) no. 4 | DOI:10.1007/s11785-021-01117-3
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