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A Class of Matrix-Valued Schrödinger Operators with Prescribed Finite-Band Spectra

Fritz Gesztesy·Lev A. Sakhnovich
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Abstract

We construct a class of matrix-valued Schrödinger operators with prescribed finite-band spectra of maximum spectral multiplicity. The corresponding matrix potentials are shown to be stationary solutions of the KdV hierarchy. The methods employed in this paper rely on matrix-valued Herglotz functions, Weyl--Titchmarsh theory, pencils of matrices, and basic inverse spectral theory for matrix-valued Schrödinger operators.

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BibTeXRIS

Fritz Gesztesy, Lev A. Sakhnovich. 2001-12-12. A Class of Matrix-Valued Schrödinger Operators with Prescribed Finite-Band Spectra. https://arxiv.org/abs/math/0112132

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