95-172 F. Gesztesy, G. Teschl
Commutation Methods for Jacobi Operators (99K, amslatex) Mar 29, 95
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Abstract. We offer two methods of inserting eigenvalues into spectral gaps of a given background Jacobi operator. The single commutation method which introduces eigenvalues into the lowest spectral gap of a given semi-bounded background Jacobi operator and the double commutation method which inserts eigenvalues into arbitrary spectral gaps. Moreover, we prove unitary equivalence of the commuted operators, restricted to the orthogonal complement of the eigenspace corresponding to the newly inserted eigenvalues, with the original background operator. Concrete applications include an explicit realization of the isospectral torus for algebro-geometric finite-gap Jacobi operators and the N-soliton solutions of the Toda and Kac-van Moerbeke lattice equations with respect to arbitrary backgrounds.

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