Spectral matrix for Sturm-Liouville operators on two-sided unbounded time scales

Abstract

We establish existence of a spectral matrix for Sturm-Liouville operators on two-sided unboundedtime scales. A Parseval equality and an expansion in eigenfunctions formula are obtained in terms of the spectral matrix. Our results unify and extend the well-known results on existence of a spectral matrix for Sturm-Liouville operators on the whole real axis and their discrete analogs. © THETA, 2013.