Fundamental solutions of pseudo-differential operators over p-adic fields

TL;DR

This paper establishes the existence of fundamental solutions for p-adic pseudo-differential operators with polynomial symbols, advancing the mathematical understanding of these operators over p-adic fields.

Contribution

It proves the existence of fundamental solutions for a class of p-adic pseudo-differential operators with polynomial symbols, a novel result in this area.

Findings

Fundamental solutions exist for p-adic pseudo-differential operators with polynomial symbols.

The results extend the theory of pseudo-differential operators in p-adic analysis.

Provides a foundation for further research in p-adic differential equations.

Abstract

We show the existence of fundamental solutions for p-adic pseudo-differential operators with polynomial symbols.