Inverse Problems And Spectral Theory

Author : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 47,7 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9783110940961

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Method of Spectral Mappings in the Inverse Problem Theory by Vacheslav A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.

Author : Hiroshi Isozaki
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 50,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834213

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Inverse Problems and Spectral Theory by Hiroshi Isozaki Pdf

This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.

Author : Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell
Publisher : SIAM
Page : 206 pages
File Size : 47,5 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713879

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An Introduction to Inverse Scattering and Inverse Spectral Problems by Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell Pdf

Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Author : V. A. Yurko
Publisher : Unknown
Page : 316 pages
File Size : 45,8 Mb
Release : 2002
Category : Inverse problems (Differential equations)
ISBN : 3110631210

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Method of Spectral Mappings in the Inverse Problem Theory by V. A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.

Author : Hiroshi Isozaki
Publisher : Springer Nature
Page : 130 pages
File Size : 47,7 Mb
Release : 2020-09-26
Category : Science
ISBN : 9789811581991

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Inverse Spectral and Scattering Theory by Hiroshi Isozaki Pdf

The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply this idea also to the Dirac equation, the Maxwell equation, and discrete Schrödinger operators on perturbed lattices. Our final topic is the boundary control method introduced by Belishev and Kurylev, which is for the moment the only systematic method for the reconstruction of the Riemannian metric from the boundary observation, which we apply to the inverse scattering on non-compact manifolds. We stress that this book focuses on the lucid exposition of these problems and mathematical backgrounds by explaining the basic knowledge of functional analysis and spectral theory, omitting the technical details in order to make the book accessible to graduate students as an introduction to partial differential equations (PDEs) and functional analysis.

Author : Jurgen Poschel
Publisher : Academic Press
Page : 192 pages
File Size : 44,9 Mb
Release : 1987-03-16
Category : Mathematics
ISBN : 0080874495

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Inverse Spectral Theory by Jurgen Poschel Pdf

Inverse Spectral Theory

Author : Alexander Kachalov,Yaroslav Kurylev,Matti Lassas
Publisher : CRC Press
Page : 309 pages
File Size : 55,5 Mb
Release : 2001-07-30
Category : Mathematics
ISBN : 9781420036220

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Inverse Boundary Spectral Problems by Alexander Kachalov,Yaroslav Kurylev,Matti Lassas Pdf

Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, the mathematical theory of inverse problems remains incomplete and needs further development to aid in the solution of many important practical problems. Inverse Boundary Spectral Problems

Author : Hiroshi Isozaki,Yaroslav Kurylev
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 2014-06
Category : Mathematics
ISBN : 4864970211

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Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds by Hiroshi Isozaki,Yaroslav Kurylev Pdf

This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hyperbolic manifolds. Based upon the classical stationary scattering theory in ℝn, the key point of the approach is the generalized Fourier transform, which serves as the basic tool to introduce and analyse the time-dependent wave operators and the S-matrix. The crucial role is played by the characterization of the space of the scattering solutions for the Helmholtz equations utilizing a properly defined Besov-type space. After developing the scattering theory, we describe, for some cases, the inverse scattering on the asymptotically hyperbolic manifolds by adopting, for the considered case, the boundary control method for inverse problems.The manuscript is aimed at graduate students and young mathematicians interested in spectral and scattering theories, analysis on hyperbolic manifolds and theory of inverse problems. We try to make it self-consistent and, to a large extent, not dependent on the existing treatises on these topics. To our best knowledge, it is the first comprehensive description of these theories in the context of the asymptotically hyperbolic manifolds.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Author : Andreas Kirsch
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 55,5 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9781441984746

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An Introduction to the Mathematical Theory of Inverse Problems by Andreas Kirsch Pdf

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.

Author : Z.S. Agranovich,V. A.. Marchenko
Publisher : Courier Dover Publications
Page : 307 pages
File Size : 44,5 Mb
Release : 2020-05-21
Category : Mathematics
ISBN : 9780486842493

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The Inverse Problem of Scattering Theory by Z.S. Agranovich,V. A.. Marchenko Pdf

This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.

Author : Manfred Möller,Vyacheslav Pivovarchik
Publisher : Springer Nature
Page : 349 pages
File Size : 42,6 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030604844

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Direct and Inverse Finite-Dimensional Spectral Problems on Graphs by Manfred Möller,Vyacheslav Pivovarchik Pdf

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.

Author : Pierre H. Berard
Publisher : Springer
Page : 284 pages
File Size : 45,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540409588

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Spectral Geometry by Pierre H. Berard Pdf

Author : V A Yurko
Publisher : CRC Press
Page : 272 pages
File Size : 53,7 Mb
Release : 2000-01-18
Category : Mathematics
ISBN : 9781482287431

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Inverse Spectral Problems for Linear Differential Operators and Their Applications by V A Yurko Pdf

Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe

Author : Khosrow Chadan,Pierre C. Sabatier
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642833175

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Inverse Problems in Quantum Scattering Theory by Khosrow Chadan,Pierre C. Sabatier Pdf

The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.

Author : K. Chadan,P. C. Sabatier
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 48,8 Mb
Release : 2013-04-18
Category : Science
ISBN : 9783662121252

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Inverse Problems in Quantum Scattering Theory by K. Chadan,P. C. Sabatier Pdf