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Research Article | Open Access

On the meromorphic continuation of the Mellin transform associated to the wave kernel on Riemannian symmetric spaces of the non-compact type

Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24231, Saudi Arabia
Institut Supérieur des Sciences Appliquées et de Technologie, Université de Sousse, 4003 Sousse, Tunisia
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Abstract

We considered the Mellin transform assigned to the convolution wave kernel associated to the Laplace-Beltrami operator on higher rank Riemannian symmetric spaces of the non-compact type. The occurrence of the analyticity strip of this transform can be deduced directly from the pointwise kernel estimates. Using the zeta function techniques, we established its meromorphic extension to the entire complex plane C with simple poles on the real line.

Keywords

Riemannian symmetric spaceswave kernelMellin transformasymptotic expansionmeromorphic continuationzeta function
CLC number: 53C35, 53Z05, 22E30, 43A85

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 14731-14746
DOI: 10.3934/math.2024716

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Cite this article:
Hassani A. On the meromorphic continuation of the Mellin transform associated to the wave kernel on Riemannian symmetric spaces of the non-compact type. AIMS Mathematics, 2024, 9(6): 14731-14746. https://doi.org/10.3934/math.2024716

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Received: 04 March 2024
Revised: 09 April 2024
Accepted: 15 April 2024
Published: 23 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)