The inverse problem according to different spectral datas for regular and singular differential operators

This thesis consists of seven chapters. In the first chapter the history of spectral theory of Sturm-Liouville, Bessel, Diffu-sion and Dirac operators were given. In the second chapter some fundemental definitions, often used in spectral theory of differential operators, were given. In the third part general form, canonic forms, asymptotic formula for eigenvalues of one-dimensional stationary Dirac operator and matrix transmutation operator of canonic Dirac operator were investigated. In the fourth chapter Bessel differential equation and basic properties of this equation were given and the isospectrality problem for Bessel operator is investigated by using transmutation operator and Gelfand-Levitan integral equation. In the fifth chapter some physical and spectral properties of the diffusion operator were given and isospectrality problem for this operator is examined and in the general case general degeneracy of the kernels is obtained by a different method. In the six and seven chapter two different problems for diccontinuous Dirac opera-tor is considered and asymptotic formulas of eigenvalues and eigenfunctions for this ope-rator were obtained.