English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

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