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An inverse problem for the Sturm-Liouville operator with nonseparable self-adjoint boundary conditions. (English. Russian original) Zbl 0728.34012

Sib. Math. J. 31, No. 6, 910-918 (1990); translation from Sib. Mat. Zh. 31, No. 6(184), 46-54 (1990).
The authors study the solution of a Sturm-Liouville problem with non- separated but selfadjoint boundary conditions. They report necessary and sufficient conditions which have to be satisfied by two sequences of real numbers such that they are spectra of two nonsimilar boundary value problems of the type mentioned. Next they determine the spectral characteristics which are necessary to recover (together with the spectrum) the boundary value problems and report the method to do this.

MSC:

34A55 Inverse problems involving ordinary differential equations
47E05 General theory of ordinary differential operators
34B24 Sturm-Liouville theory
34L99 Ordinary differential operators
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References:

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