On regularized trace formulas for weighted sturm-liouville with coefficient delta-function

In the first part of this study, information about differential operators, Sturm-Liouville operator and inverse spectral problems are given. In the second chapter, the basic definitions and theorems that are frequently used in the spectral theory of differential operators are explained. In the third chapter, the spectral theory for the Sturm-Liouville operator is introduced, the basic problems of spectral analysis are explained, the general problems about the trace formulas are given and the general information about the regularized trace formulas for the Sturm-Liouville operator is explained. Information about trace identity of a differential, spectral structure of differential operator, numerical calculation of eigenvalues, inverse problems are given. In the fourth chapter, operators are defined on the regularized trace formulas for Delta-Function coefficient weighted Sturm-Liouville problems, their spectral characteristics are mentioned and the trace problem is solved. KeyWords: Sturm-Liouville operators; Eigenvalue; Eigenfunction; Trace formulas; Weighted Sturm-Liouville problem.