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Singular expansion of the wave kernel and harmonic sums on Riemannian symmetric spaces of the non-compact type

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Názov: Singular expansion of the wave kernel and harmonic sums on Riemannian symmetric spaces of the non-compact type
Autori: Ali Hassani
Zdroj: AIMS Mathematics, Vol 10, Iss 3, Pp 4775-4791 (2025)
Informácie o vydavateľovi: American Institute of Mathematical Sciences (AIMS), 2025.
Rok vydania: 2025
Predmety: singular expansion, asymptotic expansion, riemannian symmetric spaces, wave kernel, QA1-939, harmonic sums, mellin transform, poisson kernel, Mathematics, zeta function
Popis: The Mellin transform assigned to the convolution Poisson kernel on higher rank Riemannian symmetric spaces of the non-compact type is equal to the wave kernel. This makes it possible to determine the poles and to deduce the singular expansion of this kernel by using the zeta function techniques on compact and non-compact manifolds. As a consequence, we studied the harmonic sums associated with the wave kernel. In particular, we derived its asymptotic expansion near $ 0 $ according to the Mellin-converse correspondence rule.
Druh dokumentu: Article
ISSN: 2473-6988
DOI: 10.3934/math.2025219
Prístupová URL adresa: https://doaj.org/article/efb2e0701e9c45579f54904d848501ca
Prístupové číslo: edsair.doi.dedup.....3114e15ba1795e6efb0442190a78f7ab
Databáza: OpenAIRE
Popis
Abstrakt:The Mellin transform assigned to the convolution Poisson kernel on higher rank Riemannian symmetric spaces of the non-compact type is equal to the wave kernel. This makes it possible to determine the poles and to deduce the singular expansion of this kernel by using the zeta function techniques on compact and non-compact manifolds. As a consequence, we studied the harmonic sums associated with the wave kernel. In particular, we derived its asymptotic expansion near $ 0 $ according to the Mellin-converse correspondence rule.
ISSN:24736988
DOI:10.3934/math.2025219