Characterization of Eigenvalues in Spectral Gap for Singular Differential Operators

Abstract

The spectral properties for n order differential operators are considered. When given a spectral gap (a, b) of the minimal operator T0 with deficiency index r, arbitrary m points βi (i = 1,2, …, m) in (a, b), and a positive integer function p such that , T0 has a self‐adjoint extension such that each βi (i = 1,2, …, m) is an eigenvalue of with multiplicity at least p(βi).