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

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

2001-12-12

arxiv.org/abs/math/0112132v1

Mathematics

Spectral Theory

LaTeX, 36 pages

Scientific paper

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.

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