Inverse problems for discrete Sturm-Liouville operator having Bessel-type potential

Abstract

In this paper, inverse problems are studied for Sturm-Liouville difference operators having $ \frac {p<^>{2}-1/4}{m<^>{2}} $ p2-1/4m2 type singularity. First, we define the Green's function and the corresponding Weyl function, some of their properties are investigated, and we give a method to find the potential function. Then we give the solution of the inverse nodal problem and present a constructive procedure for the solution of the inverse problem by using nodes.