Periyodik Sturm-Liouville operatörü için düz ve ters problemler

In this research, some problems of spectral analysis for periodic Sturm-Liouville operator and periodic Dirac system are investigated and explained. Firstly, periodic, semi-periodic problems and Lyapunov function (Hill's discriminant) are defined for the Sturm-Liouville operator. Then, the solution of the inverse problem for N- zoned periodic potentials is given by different methods. Second, the canonical Dirac system with periodic potential is discussed and in this case more detailed information is given about the direct and inverse problems of spectral analysis. Especially in the case of N-zone periodic potentials, new theorem of the solution of the inverse problem is proved by making use of the transformation operator and Hill discriminant. Keywords: Sturm-Liouville Operator, Periodic and Semi-Periodic boundary conditions, Transformation Operator, General Degeneracy, Dirac operator.