Characterization of Eigenvalues in Spectral Gap for Singular Differential Operators

Abstract

The spectral properties fornorder differential operators are considered. When given a spectral gap(a,b)of the minimal operatorT0with deficiency indexr, arbitrarympointsβi  (i=1,2,…,m)in(a,b), and a positive integer functionpsuch that∑i=1mp(βi)≤r,T0has a self-adjoint extensionT̃such that eachβi  (i=1,2,…,m)is an eigenvalue ofT̃with multiplicity at leastp(βi).