Inverse Spectral Problem Of Mixed Spectral Data For Sturm-Liouville Problem

The classical Sturm-Liouville operator is one of the typical representatives of differential operator theory.Its research has profound significance for the development of differential operator theory.The inverse problem of this operator can be applied to many practical problems and is used in applied mathematics.Important research areas.This paper studies the inverse problem of the Sturm-Liouville operator,and proves that the potential function has a finite number of pulse points or the potential function is a matrix-valued function,and when it is known in half the interval,only one set of spectra is needed to determine Potential function over the entire interval.The main work of this paper includes:the first chapter reviews the research history and current situation of the Sturm-Liouville inverse problem,and the main content of this article;chapter 2 introduces the basic knowledge of Sturm-Liouville operator,including spectral analysis,asymptotic solution and Weyl function;chapter 3 research When the potential function contains a finite number of pulse points in the interval[0,1]and is known in the interval[1/2,1],it is uniquely determined by combining a set of spectra[0,1]Potential function on the interval.chapter 4 when the potential function is a matrix-valued function and is known on the interval[0,1/2],a unique set of potential functions on the interval[0,1]is determined by combining a set of spectra.