Hardcover ISBN:  9780821819401 
Product Code:  SURV/72 
List Price:  $84.00 
MAA Member Price:  $75.60 
AMS Member Price:  $67.20 
Electronic ISBN:  9781470412999 
Product Code:  SURV/72.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 

Book DetailsMathematical Surveys and MonographsVolume: 72; 1999; 351 ppMSC: Primary 39; 47; 58;
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 Kacvan Moerbeke hierarchy.
Beginning with second order difference equations, the author develops discrete WeylTitchmarshKodaira 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 Kacvan Moerbeke hierarchy. Uniqueness and existence theorems for solutions, expressions for solutions in terms of Riemann theta functions, the inverse scattering transform, Bäcklund 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.ReadershipGraduate students and research mathematicians interested in finite differences and functional equations; theoretical physicists.

Table of Contents

Chapters

1. Jacobi operators

2. Foundations of spectral theory for Jacobi operators

3. Qualitative theory of spectra

4. Oscillation theory

5. Random Jacobi operators

6. Trace formulas

7. Jacobi operators with periodic coefficients

8. Reflectionless Jacobi operators

9. Quasiperiodic Jacobi operators and Riemann theta functions

10. Scattering theory

11. Spectral deformations – Commutation methods

12. The Toda system

13. The initial value problem for the Toda system

14. The Kacvan Moerbeke system


Additional Material

Reviews

[The author] does an admirable job of bringing out the ideas of the subject without getting lost in the details. This is certainly an important reference for the researcher in integrable lattices.
Mathematical Reviews


Request Review Copy

Get Permissions
 Book Details
 Table of Contents
 Additional Material
 Reviews

 Request Review Copy
 Get Permissions
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 Kacvan Moerbeke hierarchy.
Beginning with second order difference equations, the author develops discrete WeylTitchmarshKodaira 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 Kacvan Moerbeke hierarchy. Uniqueness and existence theorems for solutions, expressions for solutions in terms of Riemann theta functions, the inverse scattering transform, Bäcklund 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.
Graduate students and research mathematicians interested in finite differences and functional equations; theoretical physicists.

Chapters

1. Jacobi operators

2. Foundations of spectral theory for Jacobi operators

3. Qualitative theory of spectra

4. Oscillation theory

5. Random Jacobi operators

6. Trace formulas

7. Jacobi operators with periodic coefficients

8. Reflectionless Jacobi operators

9. Quasiperiodic Jacobi operators and Riemann theta functions

10. Scattering theory

11. Spectral deformations – Commutation methods

12. The Toda system

13. The initial value problem for the Toda system

14. The Kacvan Moerbeke system

[The author] does an admirable job of bringing out the ideas of the subject without getting lost in the details. This is certainly an important reference for the researcher in integrable lattices.
Mathematical Reviews