Jacobi Operators and Complete Integrable Nonlinear Lattices

Jacobi Operators and Complete Integrable Nonlinear Lattices
by Gerald Teschl

Publisher: American Mathematical Society 1999
ISBN/ASIN: 0821819402
ISBN-13: 9780821819401
Number of pages: 369

Description:
This book is intended to serve both as an introduction and a reference to spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric difference operators) and applications of these theories to the Toda and Kac-van Moerbeke hierarchy. Starting from second order difference equations we move on to self-adjoint operators and develop discrete Weyl-Titchmarsh-Kodaira theory, covering all classical aspects like Weyl m-functions, spectral functions, the moment problem, inverse spectral theory, and uniqueness results.