Article

**J. Reine und Angew. Math. 491, 1-15 (1997)**[DOI: 10.1515/crll.1997.491.1]

## Spectral Deformations of Jacobi Operators

### Gerald Teschl

We extend recent work concerning isospectral deformations for one-dimensional
Schrödinger operators to the case of Jacobi operators. We provide a complete
spectral characterization of a new method that constructs isospectral deformations
of a given Jacobi operator

*(H u)(n) = a(n) u(n+1) + a(n-1) u(n-1) - b(n) u(n)*. Our technique is connected to Dirichlet data, that is, the spectrum of the operator*H*on^{∞}_{n0}*l*with a Dirichlet boundary condition at^{2}(-∞,n_{0}) ⊕ l^{2}(n_{0},∞)*n*. The transformation moves a single eigenvalue of_{0}*H*and perhaps flips which side of^{∞}_{n0}*n*the eigenvalue lives. On the remainder of the spectrum the transformation is realized by a unitary operator._{0}
** MSC91:** Primary 39A10, 39A70; Secondary 34B20, 47B39

**Keywords:** *Jacobi operators, inverse spectral theory, commutation methods*

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