The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

Physics – Mathematical Physics

Scientific paper

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26 pages. Changes in the presentation of some results

Scientific paper

10.1007/s11040-008-9044-9

We present a technique for reconstructing a semi-infinite Jacobi operator in
the limit circle case from the spectra of two different self-adjoint
extensions. Moreover, we give necessary and sufficient conditions for two real
sequences to be the spectra of two different self-adjoint extensions of a
Jacobi operator in the limit circle case.

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