Non-archimedean generalized Bessel potentials and their applications

This article describes a class of pseudo-differential operators(A??)(x)=F??x?1([max?{|?1(||?||p)|,|?2(||?||p)|}]???ˆ(?)), ??D(Qpn) and ??C; here [max?{|?1(||?||p)|,|?2(||?||p)|}]?? is the symbol operator A?. These operators can be seen as generalization Bessel potentials in p-adic context. We show that family (K?)?>0 convolution kernels attached to generalized A?, ?>0, determine semigroup on Qpn. Imposing certain conditions we have K?, probability measure Moreover, will study properties corresponding Green function A? heat equations, naturally associated these operators, cooling (or loss heat) given region over time.