The Inverse Spectral Problem for Differential Operators with Nonseparated Boundary Conditions

By Vjacheslav A. Yurko. 2000

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Ž . where q x , a, d, b are real. In this paper we study an inverse spectral problem for L. It is known that for the Sturm Liouville operator l with Ž . separated boundary conditions b 0 the inverse problem has been Ž studied fairly completely see 1 7, 9, 10, 13, 15, 17 and the references . therein . The inverse problems of determining the operators with nonseparated boundary conditions from various spectral characteristics have been studied in 8, 12, 14 and other works. We mark 8 , in which an interesting method for the solution of the inverse problem in the periodic case was given. Later, in 12 this method was used for other forms of boundary conditions. In this paper we use a different method which allows one to obtain new results in the inverse problem theory for the operators with nonseparated boundary conditions. We obtain the solution of the inverse problem for the boundary value problem L, give necessary and sufficient conditions on its spectrum, and prove stability of the solution of the inverse problem. The characterization of the spectrum of L is given by two conditions: the Ž . Ž . asymptotics 1.2 and the relation 3.15 on the characteristic function

Subfields: Applied Mathematics, Mathematical Physics

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