An Introduction to Inverse Scattering and Inverse Spectral Problems

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· 제목 : An Introduction to Inverse Scattering and Inverse Spectral Problems (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미분방정식 > 미분방정식 일반
· ISBN : 9780898713879
· 쪽수 : 208쪽
· 출판일 : 1987-01-01

Foreword
Preface
Chapter 1: A Review of Basic Mathematical Tools, Lassi Päivärinta. Linear Operators on Hilbert Space
Integral Operators and the Fredholm Alternative
The Fourier Transform and the Hilbert Transform
The Unique Continuation Principle (UCP)
Unbounded Operators
The Spectrum
The Resolvent Kernel and the Fredholm Determinant
A Particle in a Box
Maxwell's Equations
References
Chapter 2: Multidimensional Inverse Scattering Theory, David Colton. Electromagnetic Scattering Problem
Bessel Functions
The Addition Formula
Green's Formula
Basic Properties of Far Field Patterns
Spectral Theory of the Far Field Operator
The Inverse Scattering Problem
The Detection and Monitoring of Leukemia
Regularization
Closing Remarks
References
Chapter 3: Inverse Sturm–Liouville Problems, William Rundell. Introduction
Preliminary Material
The Liouville Transformation
Asymptotic Expansions of the Eigenvalues and Eigenfunctions
The Inverse Problem—A Historical Look
A Completeness Result
An Important Integral Operator
Solving Hyperbolic Equations
Uniqueness Proofs
Constructive Algorithms
Modification for Other Spectral Data
Other Differential Equations
Other Constructive Algorithms
The Matrix Analogue
Another Finite-Dimensional Algorithm
Fourth-Order Problems
References
Chapter 4: Inverse Problems in Potential Scattering, Khosrow Chadan. Introduction
Physical Background and Formulation of the Inverse Scattering Problem
Scattering Theory for Partial Waves
Gel'fand–Levitan Integral Equation
Marchenko Equation
Inverse Problem on the Line
Nonlinear Evolution Equations
Closing Remarks
Appendix
References
Index.