A Class of Matrix-Valued Schr'odinger Operators with Prescribed Finite-Band Spectra

摘要

We construct a class of matrix-valued Schr\"odinger operators with prescribedfinite-band spectra of maximum spectral multiplicity. The corresponding matrixpotentials are shown to be stationary solutions of the KdV hierarchy. Themethods employed in this paper rely on matrix-valued Herglotz functions,Weyl--Titchmarsh theory, pencils of matrices, and basic inverse spectral theoryfor matrix-valued Schr\"odinger operators.