Inverse Sturm-Liouville Problems / B. M. Levitan.

Format:

Book

Author/Creator:

Levitan, B. M., author.

Language:

English

Subjects (All):

Sturm-Liouville equation.

Inverse problems (Differential equations).

Spectral theory (Mathematics).

Physical Description:

1 online resource (x, 240 pages) : illustrations

Edition:

Reprint 2018

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.

Contents:

Frontmatter

Contents

Preface

Introduction

Chapter 1. transformation operators

Chapter 2. inverse sturm-liouville problem on the half-line: determining the sturm-liouville operator from spectral function

Chapter 3. determining the regular sturm-liouville operator from two spectra

Chapter 4. the inverse problem of the quantum scattering theory

Chapter 5. the inverse problem of the quantum scattering theory at fixed energy

Chapter 6. the inverse problem of the scattering theory on the whole line

Chapter 7. inverse sturm-liouville problem on the whole line from a spectral matrix function

Chapter 8. finite-zone potentials

Chapter 9. infinite-zone potentials

Chapter 10. quasi-periodicity of finite-zone potentials

Chapter 11. quasi-periodicity of infinite-zone potentials

Chapter 12. relation between the sturm-liouville and the kortewegde vries equation

References

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Nov 2018)

ISBN:

9783110941937

3110941937

OCLC:

1046615096