Inverse Spectral Theory
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Inverse Spectral Theory
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Author : Jürgen Pöschel
language : en
Publisher:
Release Date : 1987
Inverse Spectral Theory written by Jürgen Pöschel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Spectral And Inverse Spectral Theory
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Author : Workshop Spectral and Inverse Spectral Theory
language : en
Publisher:
Release Date : 1994
Spectral And Inverse Spectral Theory written by Workshop Spectral and Inverse Spectral Theory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Inverse Spectral Theory
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Author : Jürgen Pöschel
language : en
Publisher:
Release Date : 1987
Inverse Spectral Theory written by Jürgen Pöschel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
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.
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
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.
Spectral Theory Of Canonical Systems
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Author : Christian Remling
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-21
Spectral Theory Of Canonical Systems written by Christian Remling and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Mathematics categories.
Canonical systems occupy a central position in the spectral theory of second order differential operators. They may be used to realize arbitrary spectral data, and the classical operators such as Schrödinger, Jacobi, Dirac, and Sturm-Liouville equations can be written in this form. ‘Spectral Theory of Canonical Systems’ offers a selfcontained and detailed introduction to this theory. Techniques to construct self-adjoint realizations in suitable Hilbert spaces, a modern treatment of de Branges spaces, and direct and inverse spectral problems are discussed. Contents Basic definitions Symmetric and self-adjoint relations Spectral representation Transfer matrices and de Branges spaces Inverse spectral theory Some applications The absolutely continuous spectrum
Spectral Theory And Its Applications
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Author : Bernard Helffer
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-17
Spectral Theory And Its Applications written by Bernard Helffer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-17 with Mathematics categories.
Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.
Differential Operators And Spectral Theory
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Author : M. Sh Birman
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Differential Operators And Spectral Theory written by M. Sh Birman 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 1999 with Mathematics categories.
This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrodinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.This book is aimed at graduate students and specialists in the above-mentioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive. Features: The first detailed survey of Birman's mathematical work; includes an updated bibliography. New material on the history of some branches of analysis. Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others. All original works, containing new results in fields of great current interest.
Inverse Spectral Theory For General Matrix Operators Microform
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Author : Kazem Ghanbari
language : en
Publisher: National Library of Canada = Bibliothèque nationale du Canada
Release Date : 2001
Inverse Spectral Theory For General Matrix Operators Microform written by Kazem Ghanbari and has been published by National Library of Canada = Bibliothèque nationale du Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Eigenvalues categories.