Journal of Operator Theory

Volume 70, Issue 1, Summer 2013 pp. 33-51.

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

Authors: Adil Huseynov
Author institution: Department of Mathematics, Karabuk University, 78050 Karabuk, Turkey

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2011apr03.1923
Keywords: time scale, delta derivative, nabla derivative, spectral matrix, Parseval equality, expansion in eigenfunctions

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