Uniqueness theorem of boundary inverse problems of differential operators on an interval.

Abstract

In this paper we consider a boundary inverse problem of spectral anal ysis of higher order differential operators with integro differential boundary condition s in the functional space L2(0, b). We prove a uniqueness theorem of the inverse boundary problem in th e functional space L2(0, b). The inverse problem of spectral analysis of the operator is the problem of recovering by its spectrum and some additional data. Typically, as additional spectral data of the spectral function takes the source operator, as it happened in the famous work of Israel Moiseevich Gelfand and Boris Moiseevich Levitan. In other cases serve as additional data spectra some related operators. Such an approach can be seen in the work of Leonid Shneiderman Leibenson and Viacheslav Anatol’evich Yurko . In the works of Vladimir Aleksandrovich Marchenko more spectral data is the scattering data.