On spectral properties of Sturm–Liouville operator with matrix potential

Abstract

In the work we obtain asymptotic estimates for the eigenvalues, eigenvectors and spectral projectors of a Sturm–Liouville operator with a matrix potential subject to quasi-periodic boundary conditions. The matrix potential is formed by functions square summable on the segment $[0,1]$ and the matrix of the means of the functions have simple eigenvalues. We consider also the case when the matrix of the means has a simple structure.