The inverse Sturm-Liouville problem with symmetric potentials

This study consists of three chapters. In the first chapter, some basic definitions and theories frequently used in spektral theory of differential operators are presented.In the second chapter, we deal with the Sturm Liouville problem which has discontinous points. Asymptotical formulas are obtained for eigenvalues and eigenfunctions, normalized numbers to the Sturm Liouville problem with symmetric discontinous and symmetric potential.The last chapter, inverse Sturm Liouville problem's solution is examined for finite interval with symmetric potential.Keyword. İnverse asymptotic formula; symmetric potential; spectral analysis; eigenfunction; normalized numbers.