in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...

My research lies in the intersection of three fields of mathematics: stochastic processes, representation theory and the theory of Lie groups; in particular, Lévy processes in nilpotent Lie groups. In Euclidean space, these processes are generated by a particularly nice class of operator, referred to as a pseudo-differential operator. These operators have traditionally been of interest in the s...

In this paper we study some problems related with the theory of multidimensional p-adic wavelets in connection with the theory of multidimensional p-adic pseudo-differential operators (in the p-adic Lizorkin space). We introduce a new class of n-dimensional p-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev p-adic wavelets. These wavelets (and their Fou...