p-Adic pseudodifferential operators and p-adic wavelets

TL;DR

This paper introduces a broad class of p-adic pseudodifferential operators and demonstrates that p-adic wavelets serve as their eigenbasis, advancing the mathematical understanding of p-adic analysis.

Contribution

The paper presents a new class of p-adic pseudodifferential operators and establishes p-adic wavelets as their eigenvectors, providing novel tools for p-adic analysis.

Findings

p-adic wavelets form an eigenbasis for the new operators

Introduction of a wide class of p-adic pseudodifferential operators

Enhanced understanding of p-adic spectral theory

Abstract

We introduce a new wide class of p-adic pseudodifferential operators. We show that the basis of p-adic wavelets is the basis of eigenvectors for the introduced operators.