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arXiv · 2401.07146

The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group

J. P. Velasquez-Rodriguez
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Abstract

Let $p>2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$-adic integers. As an application, we consider directional Vladimirov-Taibleson derivatives, and some polynomials in these operators. In particular, we calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it provides a non-trivial example of a sub-elliptic operator on compact graded $p$-adic Lie groups.

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BibTeXRIS

J. P. Velasquez-Rodriguez. 2024-01-13. The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group. https://arxiv.org/abs/2401.07146

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