[PDF] Method Of Spectral Mappings In The Inverse Problem Theory eBook

Author : V. A. Yurko
Publisher :
Page : 316 pages
File Size : 45,41 MB
Release : 2002
Category : Inverse problems (Differential equations)
ISBN : 9783110631210

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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 : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 43,75 MB
Release : 2013-10-10
Category : Mathematics
ISBN : 3110940965

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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 :
Page : 0 pages
File Size : 31,93 MB
Release : 2014-06
Category : Mathematics
ISBN : 9784864970211

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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 : G. Freiling
Publisher : Nova Biomedical Books
Page : 324 pages
File Size : 13,44 MB
Release : 2001
Category : Mathematics
ISBN :

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This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. 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 sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.

Author : Vladimir G. Romanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 49,66 MB
Release : 2014-10-10
Category : Mathematics
ISBN : 3110943840

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This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.

Author : Jurgen Poschel
Publisher : Academic Press
Page : 209 pages
File Size : 37,80 MB
Release : 1987-03-16
Category : Mathematics
ISBN : 0080874495

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Inverse Spectral Theory

Author : Sergey I. Kabanikhin
Publisher : Walter de Gruyter
Page : 188 pages
File Size : 41,91 MB
Release : 2013-04-09
Category : Mathematics
ISBN : 3110960710

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The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Author : Michael V. Klibanov
Publisher : Walter de Gruyter
Page : 292 pages
File Size : 46,86 MB
Release : 2012-04-17
Category : Mathematics
ISBN : 3110915545

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In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.

Author : Mikhail M. Lavrent'ev
Publisher : Walter de Gruyter
Page : 288 pages
File Size : 39,87 MB
Release : 2012-05-07
Category : Mathematics
ISBN : 3110915529

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This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Author : Mikhail M. Lavrent'ev
Publisher : Walter de Gruyter
Page : 697 pages
File Size : 48,6 MB
Release : 2011-12-22
Category : Mathematics
ISBN : 3110960729

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This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.