Direct and inverse spectral problems for discrete Sturm-Liouville problem with generalized function potential

Abstract

In this work, we study the inverse problem for difference equations which are constructed by the Sturm-Liouville equations with generalized function potential from the generalized spectral function (GSF). Some formulas are given in order to obtain the matrix J, which need not be symmetric, by using the GSF and the structure of the GSF is studied.MSC: Primary 39A12; 34A55; 34L15

Inverse scattering problem with Levinson formula for eigenparameter‐dependent discrete Sturm–Liouville equation

“…Conversely, obtaining the potential function according to the scattering data is called an inverse problem of scattering theory. In this manner, a direct and inverse Sturm–Liouville problem with generalized potential function has been studied in Bala et al 20 Also, the discrete Sturm–Liouville problem for symmetric potential with Dirichlet boundary conditions has been considered in Bohner and Koyunbakan 21 taking into account the weight numbers and symmetric potential. Some inverse scattering theories for Sturm–Liouville problems including uniqueness of the solution and continuity of scattering function have been given in previous studies 22–28 …”

Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula

“…Huseynov in [15,16], respectively. Bala et al are studied inverse spectral problem for almost symmetric tridiagonal matrices from generalized spectral function in [17] and they examined inverse spectral problems for same matrices from spectral data and two spectra in [18]. Finite dimensional inverse problems are investigated by H. Huseynov in [19].…”