**Spectral Methods for Operators of Mathematical Physics**

J. Janas, P. Kurasov, and S. Naboko (eds.), 151-154, Oper. Theory Adv. Appl.,

**154**, Birkhäuser, Basel, 2004.

## Reconstructing Jacobi Matrices from Three Spectra

### J. Michor and G. Teschl

**Keywords:** Jacobi matrices, spectral theory, trace formulas, Hochstadt's theorem.

**Abstract:**
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.

**MSC:**
Primary 36A10, 39A70; Secondary 34B24, 34L05.

**ESI Preprint** 1235

**
arXiv:math/0211051v1**

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