A boundary inverse problem for a second order differential operator
International Journal of Mathematics and Physics
In this paper we investigate a boundary inverse problem of a second order differential operator with integral boundary conditions in L � ��� ��, where � � �. A boundary inverse problem of spectral analysis is the problem of recovering boundary conditions of the operator by its spectrum and some additional data. Usually, as the additional spectral data takes the spectral function of the operator as it occurred in the famous work of I.M. Gelfand and B.M. Levitan. In other cases, as additional
... , as additional data perform spectra of some related operators. We research inverse problem of spectral analysis of second order differential operators with integro-differential boundary conditions. In this case, it is necessary to find from the spectral data not only coefficients of the differential expression, also, we need to find boundary functions of the integro-differential boundary conditions. Coefficient inverse problems are well studied. Therefore in this paper we study the issue of reconstruction of boundary functions. As a main result a uniqueness theorem of the inverse boundary problem in L � ��� �� was proved.