p-Adic Spherical Coordinates and Their Applications

TL;DR

This paper develops p-adic spherical coordinates on $\\mathbb{Q}_p^n$, enabling new descriptions of distributions and decompositions of p-adic Lévy processes, advancing the understanding of p-adic harmonic analysis.

Contribution

It introduces a novel p-adic spherical coordinate system and applies it to describe homogeneous distributions and decompose p-adic Lévy processes.

Findings

Description of homogeneous distributions on p-adic spaces

Skew product decomposition of p-adic Lévy processes

Extension of spherical coordinate concepts to p-adic analysis

Abstract

On the space $\mathbb Q_p^n$, where $p\ne 2$ and $p$ does not divide $n$, we construct a p-adic counterpart of spherical coordinates. As applications, a description of homogeneous distributions on $\mathbb Q_p^n$ and a skew product decomposition of p-adic L\'evy processes are given.