Sturm Liouville operators and applications Edition of 1986 1st Edition by Marchenko, Vladimir Aleksandrovich ISBN 978-0821853160 0821853160

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Product details: 

ISBN 10:  0821853160

ISBN 13: 978-0821853160

Author: Marchenko, Vladimir Aleksandrovich

A foundational and rigorous text in spectral analysis, Marchenko’s Sturm–Liouville Operators and Applications delivers a unified treatment of classical Sturm–Liouville theory, inverse scattering, and integrable systems, enriched in the revised edition by a new chapter on the stability of inverse reconstructions.

Table of contents: 

Chapter 1

THE STURM-LIOUVILLE EQUATION AND TRANSFORMATION OPERATORS..

1. Riemann’s Formula

2. Transformation Operators

3. The Sturm-Liouville Boundary Value Problem on a Bounded Interval

4. Asymptotic Formulas for Solutions of the Sturm-Liouville Equation

5. Asymptotic Formulas for Eigenvalues and Trace Formulas.

Chapter 2

THE STURM-LIOUVILLE BOUNDARY VALUE PROBLEM ON THE HALF LINE

1. Some Information on Distributions

2. Distribution-Valued Spectral Functions

3. The Inverse Problem

4. The Asymptotic Formula for the Spectral Functions of Symmetric Boundary Value Problems and the Equiconvergence Theorem….

Chapter 3

THE BOUNDARY VALUE PROBLEM OF SCATTERING THEORY.

1. Auxiliary Propositions

2. The Parseval Equality and the Fundamental Equation

3. The Inverse Problem of Quantum Scattering Theory..

4. Inverse Sturm-Liouville Problems on a Bounded Interval…

5. The Inverse Problem of Scattering Theory on the Full Line

Chapter 4 NONLINEAR EQUATIONS..

1. Transformation Operators of a Special Form..

2. Rapidly Decreasing Solutions of the Korteweg-de Vries Equation

3. Periodic Solutions of the Korteweg-de Vries Equation

4. Explicit Formulas for Periodic Solutions of the Korteweg-de Vries Equation….

Chapter 5

STABILITY OF INVERSE PROBLEMS.

1. Problem Formulation and Derivation of Main Formulas.

2. Stability of the Inverse Scattering Problem

3. Error Estimate for the Reconstruction of a Boundary Value Problem from its Spectral Function Given on the Set (-∞, N²) Only…

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