Some properties of the resolvent of Sturm-Liouville operators on unbounded time scales

Abstract

In this article, we investigate the resolvent operator of Sturm-Liouville problem on unbounded time scales. We obtain integral representations for the resolvent of this operator. Later, we discuss some properties of the resolvent operator, such as Hilbert-Schmidt’s kernel property and compactness. Finally, we give a formula for the Titchmarsh-Weyl function of the Sturm-Liouville problem on unbounded time scales. MSC 2010. 34N05, 34L05, 47A10.