Fundamental solution of the Vladimirov-Taibleson operator on noncommutative Vilenkin groups

Autor:	delgado, Julio, Velasquez-Rodriguez, Juan Pablo
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	The fundamental solution and the heat semigroup of the Vladimirov-Taibleson operator on constant-order noncommutative Vilenkin groups are obtained, together with some estimates on the associated heat kernel. We also show the existence of a fundamental solution for the "Vladimirov Laplacian" on the $p$-adic Heisenberg group and the $p$-adic Engel group, and discuss possible extensions of our results to more general homogeneous operators on graded $p$-adic Lie groups.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.07133 Zobrazit plný text záznamu View this record from Arxiv