Non-archimedean generalized Bessel potentials and their applications

Abstract

This article describes a class of pseudo-differential operatorsis the symbol of the operator A α . These operators can be seen as a generalization of the Bessel potentials in the p-adic context. We show that the family (Kα) α>0 of convolution kernels attached to generalized Bessel potentials A α , α > 0, determine a convolution semigroup on Q n p . Imposing certain conditions we have that Kα, α > 0, is a probability measure on Q n p . Moreover, we will study certain properties corresponding to the Green function of the operator A α and we show that heat equations, naturally associated to these operators, describes the cooling (or loss of heat) in a given region over time.