Spectral Analysis of Differential Operators with Involution and Operator Groups

Abstract

We study the spectral properties of differential operators with involution of the following two types: operators with involution multiplying the potential and operators with involution multiplying the derivative. The similar operator method is used to obtain a refined asymptotics of the eigenvalues and eigenvectors of such operators. These asymptotics are used to derive asymptotic formulas for the operator groups generated by the operators in question. These operator groups can be used to describe mild solutions of the corresponding mixed problems.