A Class of Matrix-Valued Schr\"odinger Operators with Prescribed Finite-Band Spectra
Spectral Theory
2007-05-23 v1
Abstract
We construct a class of matrix-valued Schr\"odinger 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 Schr\"odinger operators.
Keywords
Cite
@article{arxiv.math/0112132,
title = {A Class of Matrix-Valued Schr\"odinger Operators with Prescribed Finite-Band Spectra},
author = {Fritz Gesztesy and Lev A. Sakhnovich},
journal= {arXiv preprint arXiv:math/0112132},
year = {2007}
}
Comments
LaTeX, 36 pages