Asymptotic stability of the spectra of generalized indefinite strings

Abstract

This paper focuses on the asymptotic stability of the spectra of generalized indefinite strings (GISs). A unitarily equivalent linear relation is introduced for GISs. It is shown that the solutions of the corresponding differential equations are continuously dependent on distributions and measures under certain conditions. Using these results, the convergence of unitarily equivalent linear relations for GISs is discussed. By the perturbation theory to closed linear relations, an asymptotic stability result concerning the spectra of linear relations for GISs is obtained.