Spectral theory of the singular Dirac operator

This thesis consists of seven chapters.In the first chapter; the history of spectral theory (well and ill-posed problem) Sturm-Liouville and Dirac operators were given.In the second chapter; some fundemantal definitions often used in the spectral theory differential operators were given.In the third chapter; one dimensional stationary and canonic forms of Dirac operator, asymptotic formula for eigenvalues, matrix transformation operator for canonic Dirac operators, the statement of norming constants in terms of two spectrums, asymptotic formula for norming constants and inverse problem according to two spectrums were studied.In the fourth chapter; singular Dirac operator, inverse problem according to two spectrum and asymptotic statements for norming constants were obtained.In the fifth chapter; in semi-axis inverse problem according to two spectrums for Dirac operator was examined.In the sixth and the seventh chapters that constitute the original part of our study, the general degenerate of transformation operator for singular Dirac operator and well-posedness problem were studied, respectively.Key Words: Spectrum, Inverse problem, Dirac operator, eigenvalue, eigenvector function,General degenerate, Well-posedness.