Spectral Decompositions of Selfadjoint Relations in Pontryagin Spaces and Factorizations of Generalized Nevanlinna Functions

Abstract

Selfadjoint relations in Pontryagin spaces do not possess a spectral family completely characterizing them in the way that selfadjoint relations in Hilbert spaces do. Here it is shown that a combination of a factorization of generalized Nevanlinna functions with the standard spectral family of selfadjoint relations in Hilbert spaces can function as a spectral family for selfadjoint relations in Pontryagin spaces. By this technique additive decompositions are established for generalized Nevanlinna functions and selfadjoint relations in Pontryagin spaces.