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A Class of Matrix-valued Schrödinger Operators with Prescribed Finite-band Spectra

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Reproducing Kernel Spaces and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 143))

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 Her-glotz functions, Weyl— Titchmarsh theory, pencils of matrices, and basic inverse spectral theory for matrix-valued Schrödinger operators.

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  1. Department of Mathematics, University of Missouri Columbia, MO, 65211, USA

    Fritz Gesztesy

  2. 735 Crawford Ave, Brooklyn, NY, 11223, USA

    Lev A. Sakhnovich

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  1. Fritz Gesztesy
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  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105, Beer Sheva, Israel

    Daniel Alpay

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Gesztesy, F., Sakhnovich, L.A. (2003). A Class of Matrix-valued Schrödinger Operators with Prescribed Finite-band Spectra. In: Alpay, D. (eds) Reproducing Kernel Spaces and Applications. Operator Theory: Advances and Applications, vol 143. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8077-0_7

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  • DOI: https://doi.org/10.1007/978-3-0348-8077-0_7

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