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Dynamic inverse problem for Jacobi matrices


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  • We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite Jacobi matrix. We derive discrete analogs of Krein equations and answer a question on the characterization of dynamic inverse data. As a consequence we obtain a necessary and sufficient condition for a measure on a real line to be a spectral measure of a semi-infinite discrete Schrödinger operator.

    Mathematics Subject Classification: Primary: 35R30, 93B30; Secondary: 39A12, 35C15, 35P99.


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