Abstract

Fritz Gesztesy

University of Missouri

Title: On algebro-geometric matrix-valued KdV solutions

Abstract: We construct Schr\"odinger operators with algebro-geometric matrix-valued potentials associated with a prescribed finite-band spectrum of maximal multiplicity. The principal techniques employed are matrix-valued Herglotz functions and self-adjoint pencils of matrices. We derive matrix-valued trace formulas for KdV invariants and sketch connections with the nonabelian KdV hierarchy.

This is based on joint work with L. Sakhnovich

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