January 7, 2002
Victor Vinnikov
Title: Functional models for almost periodic Jacobi matrices and a generalization of the Toda hierarchy
It is well known that for an almost periodic Jacobi matrix whose spectrum consists of a finite union of intervals, the evolution equations of the Toda hierarchy correspond to linear evolution equations in certain directions on a (finite dimensional) torus. We establish a similar result for a much wider class of evolution equations and an arbitrary almost periodic Jacobi matrix whose spectrum (containing, in general, infinitely many gaps) satisfies the so called homogeneity condition. Our solution arises naturally within the framework of functional models on an associated Riemann surface.