Inverse Problems And Spectral Theory
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Inverse Problems And Spectral Theory
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Author : Hiroshi Isozaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Inverse Problems And Spectral Theory written by Hiroshi Isozaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Inverse Spectral Theory
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Author : Jurgen Poschel
language : en
Publisher: Academic Press
Release Date : 1987-03-16
Inverse Spectral Theory written by Jurgen Poschel and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-16 with Mathematics categories.
Inverse Spectral Theory
An Introduction To Inverse Scattering And Inverse Spectral Problems
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Author : Khosrow Chadan
language : en
Publisher: SIAM
Release Date : 1997-01-01
An Introduction To Inverse Scattering And Inverse Spectral Problems written by Khosrow Chadan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
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.
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.
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.
Method Of Spectral Mappings In The Inverse Problem Theory
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Author : V. A. Yurko
language : en
Publisher:
Release Date : 2002
Method Of Spectral Mappings In The Inverse Problem Theory written by V. A. Yurko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Inverse problems (Differential equations) categories.
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.
Inverse Boundary Spectral Problems
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Author : Alexander Kachalov
language : en
Publisher: CRC Press
Release Date : 2001-07-30
Inverse Boundary Spectral Problems written by Alexander Kachalov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-30 with Mathematics categories.
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
Gaussian Processes Function Theory And The Inverse Spectral Problem
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Author : Harry Dym
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Gaussian Processes Function Theory And The Inverse Spectral Problem written by Harry Dym and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.
The Inverse Problem Of Scattering Theory
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Author : Z.S. Agranovich
language : en
Publisher: Courier Dover Publications
Release Date : 2020-05-21
The Inverse Problem Of Scattering Theory written by Z.S. Agranovich and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Mathematics categories.
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.
Inverse Spectral And Scattering Theory
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Author : Hiroshi Isozaki
language : en
Publisher: Springer Nature
Release Date : 2020-09-26
Inverse Spectral And Scattering Theory written by Hiroshi Isozaki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-26 with Science categories.
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.
Inverse And Ill Posed Problems
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Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Inverse And Ill Posed Problems written by Sergey I. Kabanikhin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.