The Inverse Spectral Problem Of Regular Dirac Operator

The inverse spectral problem of Dirac differential operator originated in re-searching the variation of free electrons in generalized quantum theory. As the development of cross subject such as mathematical physics, geophysics and system science, it has gotten more and more attention and became one of popular topic in applied mathematics. In this paper, we research how to determine and recover a po-tential in different spectral information. Here, it can be divided into two categories: one is regular boundary-value problem, another is problem with spectral parameter contained in the boundary conditions. The main works are given as follows:In the first chapter, we introduce the research background, significance, and advance of Dirac system, and review the basic concept of Dirac problem, which make preparation for the inverse spectral problem.In the second chapter, we are concerned with the inverse three spectral problem with spectral parameter in the boundary conditions. The uniqueness theorem and its proof are given.In the third chapter, the half inverse spectral problem of regular Dirac operator is considered. We obtain that the whole potential can be uniquely determined by a group of Dirichlet specturm when the potential in half of the interval are known.In the last chapter, the inverse spectral problem based on the blend spectral data, and with spectral parameter in the boundary conditions are considered. When potential in half of the interval are known, the potential can be uniquely determined.