Jacobi Operators and Completely Integrable Nonlinear Lattices
Regular price
€122.99
14 days return policy
Shipping & Delivery
A01=American Mathematical Society
Author_American Mathematical Society
Category=PBKF
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Product details
- ISBN 9780821819401
- Weight: 857g
- Publication Date: 30 Oct 1999
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
This volume can serve as an introduction and a reference source on spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric difference operators) and applications of those theories to the Toda and Kac-van Moerbeke hierarchy. Beginning with second order difference equations, the author develops discrete Weyl-Titchmarsh-Kodaira theory, covering all classical aspects, such as Weyl $m$-functions, spectral functions, the moment problem, inverse spectral theory, and uniqueness results.Teschl then investigates more advanced topics, such as locating the essential, absolutely continuous, and discrete spectrum, subordinacy, oscillation theory, trace formulas, random operators, almost periodic operators, (quasi-)periodic operators, scattering theory, and spectral deformations. Utilizing the Lax approach, he introduces the Toda hierarchy and its modified counterpart, the Kac-van Moerbeke hierarchy. Uniqueness and existence theorems for solutions, expressions for solutions in terms of Riemann theta functions, the inverse scattering transform, Backlund transformations, and soliton solutions are derived. This text covers all basic topics of Jacobi operators and includes recent advances. It is suitable for use as a text at the advanced graduate level.
