JOURNAL OF OPERATOR THEORY, cilt.70, ss.33-51, 2013 (SCI İndekslerine Giren Dergi)
We establish existence of a spectral matrix for Sturm-Liouville operators on two-sided unbounded time 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.