Pseudo-differential Operators with Semi-Quasielliptic Symbols Over p-adic Fields

TL;DR

This paper investigates pseudo-differential equations with semi-quasielliptic symbols over p-adic fields, establishing solution spaces and demonstrating a regularization effect for certain parabolic equations.

Contribution

It introduces the space of infinitely pseudo-differentiable functions related to semi-quasielliptic operators and proves regularization effects over p-adic fields.

Findings

Existence of solutions in specific function spaces

Introduction of infinitely pseudo-differentiable function space

Regularization effect for p-adic parabolic equations

Abstract

In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable functions with respect to a semi-quasielliptic operator. By using these spaces we show the existence of a regularization effect for certain parabolic equations over p-adics.