Asymptotics of eigenvalues for differential operators of fractional order

Abstract

Abstract In this paper we deal with a linear combination of a second order uniformly elliptic operator and the Kipriyanov fractional differential operator. We use a novel method based on properties of a real component to study such type of operators. We conduct the classification of the operators by belonging of their resolvent to the Schatten-von Neumann class and formulate the sufficient condition for the completeness of the root functions system. Finally we obtain an asymptotic formula.