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∞n0 on l2 (-∞,n0) ⊕ l2 (n0,∞) with a
Dirichlet boundary condition at n0. The transformation
moves a single eigenvalue of H∞n0 and perhaps flips which side of
n0 the eigenvalue lives. On the remainder of the spectrum the transformation
is realized by a unitary operator.
MSC91: Primary 39A10, 39A70; Secondary 34B20, 47B39
Keywords: Jacobi operators, inverse spectral theory, commutation methods
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