Characterization of Eigenvalues in Spectral Gap for Singular Differential Operators

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 ∑i=1mp(βi)≤r, T0 has a self-adjoint extension T̃ such that each βi  (i=1,2,…,m) is an eigenvalue of T̃ with multiplicity at least p(βi)