Distribution of the eigenvalues of singular differential operators in a space of vector-functions

Abstract

. A significant part of B. M. Levitan’s scientific activity dealt with questions on the distribution of the eigenvalues of differential operators [1]. To study the spectral density, he mainly used Carleman’s method, which he perfected. As a rule, he considered scalar differential operators. The purpose of this paper is to study the spectral density of differential operators in a space of vector-functions. The paper consists of two sections. In the first we study the asymptotics of a fourth-order differential operator