Singular point-like perturbations of the Bessel operator in a Pontryagin space

The spectral problem for the Bessel equation of order v on (0, infinity) in the case 0 < v < 1 is closely related to the Nevanlinna function Q(z) = - pi( - z)(v)/(2 sin pi v). If v > 1 and v not equal 2, 3,..., this function belongs to the generalized Nevanlinna class N-m, m = [v+1/2]. A natural que stion appears: To what spectral problem does this function correspond! We a nswer this and related questions using Pontryagin space operator realizatio ns of suitable singular point-like perturbations of the Bessel operator. In this paper we discuss the spectra of these realizations and we derive eige nfunction expansions via related wave operators. (C) 2000 Academic Press.