Inverse problem with respect to two spectra for regüler and singular differential operators

In the spectral theory of differential operators, the problem of finding potential function by using spectral datas is called inverse problem. In an inverse problem, if the potential difference becames sufficiently small when the difference between the charec-teristics was changed as suficiently small, this problem is called as stable(wellposed).This study consists of five chapters.In the first chapter, the history of spectral theory a Sturm-Liouville, Dirac and diffusion operators are presented.In the second chapter some fundamental definitions and theorem, often used in spectral theory of differential operators, are given.In the third chapter, the asymptotic formulas for eigenvalues and eigenfunctions, the ortogonality of the eigenfunctions, the reality of the eigenvalues and transformation operator for Sturm-Liouville operator are shown. In particular the formula is given for difference of potantials.In the fourth and fifth chapters, we investigated the stability of inverse problem for Dirac and diffusion operators ,respectively. We obtained some formulas for potential difference.Keywords: Spectrum, Inverse Sturm-Liouville Problem, Dirac Operator, Diffusion Operator, Stability(Wellposedness).