Herglotz's theorem for Jacobi-Dunkl positive definite sequences-Reference-Cited by-同舟云学术

Herglotz's theorem for Jacobi-Dunkl positive definite sequences

Published:2021-06-01 Issue:3 Volume:71 Page:655-666
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Chouchene Frej¹,Haouala Iness¹

Affiliation:

1. Department of Mathematics , Higher School of Sciences and Technology of Hammam Sousse, University of Sousse , Sousse , Tunisia

Abstract

Abstract In this work, we introduce the notion of Jacobi-Dunkl positive definite sequences using the properties of the discrete Jacobi-Dunkl translation. Then, we establish the analogous of Herglotz’s theorem to characterize these sequences.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2021-0011/pdf

Reference16 articles.

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2. Chouchene, F.: Harmonic analysis associated with the Jacobi-Dunkl operator on ]− π2,π2$\begin{array}{} \displaystyle \frac{\pi}{2},\frac{\pi}{2} \end{array}$[, J. Comput. Appl. Math. 178 (2005), 75–89.

3. Chouchene, F.: Bounds, asymptotic behavior and recurrence relations for the Jacobi-Dunkl polynomials, International Journal of Open Problems Complex Analysis 6(1) (2014), 49–77.

4. Chouchene, F.: Recurrence and Christoffel-Darboux formulas for the Jacobi-Dunkl polynomials and applications, Commun. Math. Anal. 16(1) (2014), 123–142.

5. Einsiedler, M.—Ward, T.: Functional analysis, spectral theory, and applications. Grad. Texts in Math. 276, Springer International Publishing AG, 2017.

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