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Author : A P Katchalov,Y Kurylev
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 2000-10-01
Category : Electronic
ISBN : 0582381339
Author : Alexander Kachalov,Yaroslav Kurylev,Matti Lassas
Publisher : Chapman and Hall/CRC
Page : 260 pages
File Size : 49,6 Mb
Release : 2001-07-30
Category : Mathematics
ISBN : 1584880058
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 develop a rigorous theory for solving several types of inverse problems exactly. In it, the authors consider the following: "Can the unknown coefficients of an elliptic partial differential equation be determined from the eigenvalues and the boundary values of the eigenfunctions?" Along with this problem, many inverse problems for heat and wave equations are solved. The authors approach inverse problems in a coordinate invariant way, that is, by applying ideas drawn from differential geometry. To solve them, they apply methods of Riemannian geometry, modern control theory, and the theory of localized wave packets, also known as Gaussian beams. The treatment includes the relevant background of each of these areas. Although the theory of inverse boundary spectral problems has been in development for at least 10 years, until now the literature has been scattered throughout various journals. This self-contained monograph summarizes the relevant concepts and the techniques useful for dealing with them.
Author : Alexander Kachalov,Yaroslav Kurylev,Matti Lassas
Publisher : CRC Press
Page : 309 pages
File Size : 45,9 Mb
Release : 2001-07-30
Category : Mathematics
ISBN : 9781420036220
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 : V A Yurko
Publisher : CRC Press
Page : 272 pages
File Size : 55,9 Mb
Release : 2000-01-18
Category : Mathematics
ISBN : 9781482287431
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,David Colton,Lassi P?iv?rinta,William Rundell
Publisher : SIAM
Page : 206 pages
File Size : 43,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713879
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 : Hiroshi Isozaki
Publisher : Springer Nature
Page : 130 pages
File Size : 46,7 Mb
Release : 2020-09-26
Category : Science
ISBN : 9789811581991
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 : Hiroshi Isozaki
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 54,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834213
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 : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 50,6 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9783110940961
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 : Kenrick Bingham,Yaroslav V. Kurylev,E. Somersalo
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662089668
In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.
Author : Jurgen Poschel
Publisher : Academic Press
Page : 192 pages
File Size : 48,8 Mb
Release : 1987-03-16
Category : Mathematics
ISBN : 0080874495
Inverse Spectral Theory
Author : Pierre H. Berard
Publisher : Springer
Page : 284 pages
File Size : 52,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540409588
Author : Plamen Stefanov,András Vasy,Maciej Zworski
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 52,6 Mb
Release : 2014-05-05
Category : Mathematics
ISBN : 9781470410797
This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.
Author : Manfred Möller,Vyacheslav Pivovarchik
Publisher : Springer Nature
Page : 349 pages
File Size : 52,5 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030604844
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 : V. A. Yurko
Publisher : Unknown
Page : 316 pages
File Size : 44,8 Mb
Release : 2002
Category : Inverse problems (Differential equations)
ISBN : 3110631210
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 : Vesselin Petkov,Luchezar N. Stoyanov
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 48,5 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015025208268
The behaviour of reflecting rays plays an essential role in many problems of mathematical physics. This book studies different geometric properties of reflecting rays for manifolds with smooth boundary and their applications to different inverse spectral and scattering problems. This is a developing area in which the authors have made important contributions. Results concerning the particular problems studied and which arise in several important domains of modern physics are presented. Some chapters concerning the generic properties of reflecting rays can be used for courses for graduate students.
