Singular Point-like Perturbations of the Bessel Operator in a Pontryagin Space

The spectral problem for the Bessel equation of order ν on (0, ∞) in the case 0<ν<1 is closely related to the Nevanlinna function Q(z)=−π(−z)ν/(2 sin πν). If ν>1 and ν≠2, 3, ..., this function belongs to the generalized Nevanlinna class Nm, m=[ ]. A natural question appears: To what spectral problem does this function correspond? We answer this and related questions using Pontryagin space operator realizations of suitable singular point-like perturbations of the Bessel operator. In this paper we discuss the spectra of these realizations and we derive eigenfunction expansions via related wave operators.