The Inverse Spectral Problem For Discrete And Continuous Krein String Equation

The inverse spectral problem of Krein string equation is mainly concerned with the uniqueness and reconstruction of the equation under the condition that spectral datas are given.The research of this problem not only has great significance in mathematics but also has a wide and direct application in physics and natural science.Therefore,the inverse spectral problem of the Krein string equation has gotten more and more attention and becomes a hot topic in applied mathematics reseached by many mathematicians.In the paper we will study discrete and continuous Krein string equation's inverse problem.The discrete Krein string equation refers to Jacobi matrices and continous Krein string equation refers to regular string equation.The main works are given as follows:In the first chapter,the relationships between Krein string equation,Jacobi matrices and regular string equation are introduced.The inverse spectral problem's research background,meaning and current situation between Jacobi matrices and the regular string equation are given.In the second chapter,inverse problem of Jacobi matrices is considered.Under several special disturbances,the inverse spectral theorem of Jacobi matrices by using gained eigenvalues is proved.At the same time the paper illustrate the application of the theorem in mass-spring system which turn out to be unique and can be constructed.In the third chapter,the inverse spectral problem of regular string equation under general separation type self adjoint boundary condition is considered.Some important conclusions of nodal data of regular string equation are provided,and the reconstruction of the density function is derived.