in Spectral Methods for Operators of Mathematical Physics, J. Janas (ed.) et al., 151-154, Oper. Theory Adv. Appl. 154, 2004 [DOI: 10.1007/978-3-0348-7947-7_9]

Reconstructing Jacobi Matrices from Three Spectra

Johanna Michor and Gerald Teschl

Cut a Jacobi matrix into two pieces by removing the n-th column and n-th row. We give necessary and sufficient conditions for the spectra of the original matrix plus the spectra of the two submatrices to uniquely determine the original matrix. Our result contains Hochstadt's theorem as a special case.

MSC91: Primary 36A10, 39A70; Secondary 34B24, 34L05
Keywords: Jacobi matrices, spectral theory, trace formulas, Hochstadt's theorem

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