Non-Archimedean Pseudodifferential Operators and Feller Semigroups

Abstract

In this article we study a large class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions.We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we introduce a new class of anisotropic Sobolev spaces, which are the natural domains for the operators considered here.We also study the Cauchy problem for certain pseudodifferential equations.