Fritz Gesztesy and Lev A. Sakhnovich
A Class of Matrix-Valued Schr\"odinger Operators with Prescribed
Finite-Band Spectra
(125K, LaTeX)
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.