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Author : Alex Christopher Woo
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.F/5 ( download)
Download or read book Scattering Theory on Real Hyperbolic Spaces and Their Compact Perturbations written by Alex Christopher Woo and published by . This book was released on 1980 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bettina Erika Christina Wiskott
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.F/5 ( download)
Download or read book Scattering Theory and Spectral Representation of Short-range Perturbation in Hyperbolic Space written by Bettina Erika Christina Wiskott and published by . This book was released on 1982 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter D Lax
Publisher : Springer Science & Business Media
ISBN 13 : 9780387229263
Total Pages : 620 pages
Book Rating : 4.2/5 (292 download)
Download or read book Selected Papers II written by Peter D Lax and published by Springer Science & Business Media. This book was released on 2005-05-20 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.
Author : Vesselin Petkov
Publisher :
ISBN 13 :
Total Pages : 346 pages
Book Rating : 4.3/5 (91 download)
Download or read book Scattering Theory for Hyperbolic Operators written by Vesselin Petkov and published by . This book was released on 1987 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V. Petkov
Publisher : Elsevier
ISBN 13 : 0080875424
Total Pages : 391 pages
Book Rating : 4.0/5 (88 download)
Download or read book Scattering Theory for Hyperbolic Operators written by V. Petkov and published by Elsevier. This book was released on 1989-11-20 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering Theory for dissipative and time-dependent systems has been intensively studied in the last fifteen years. The results in this field, based on various tools and techniques, may be found in many published papers. This monograph presents an approach which can be applied to spaces of both even and odd dimension. The ideas on which the approach is based are connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator W which exploits the decay of the local energy of the perturbed and free systems. Some inverse scattering problems for time-dependent potentials, and moving obstacles with an arbitrary geometry, are also treated in the book.
Author :
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.:/5 (3 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ian W. Knowles
Publisher : Springer
ISBN 13 : 354047983X
Total Pages : 517 pages
Book Rating : 4.5/5 (44 download)
Download or read book Differential Equations and Mathematical Physics written by Ian W. Knowles and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory.
Author : AlexandreJ. Chorin
Publisher : Springer Science & Business Media
ISBN 13 : 1461395836
Total Pages : 345 pages
Book Rating : 4.4/5 (613 download)
Download or read book Wave Motion: Theory, Modelling, and Computation written by AlexandreJ. Chorin and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 60th birthday of Peter Lax was celebrated at Berkeley by a conference entitled Wave Motion: theory, application and computation held at the mathematical Sciences Research Institute, June 9-12, 1986. Peter Lax has made profound and essential contributions to the topics described by the title of the conference, and has also contributed in important ways to many other mathematical subjects, and as a result this conference volume dedicated to him includes research work on a variety of topics, not all clearly related to its title.
Author : Hassan Emamirad
Publisher : Springer Nature
ISBN 13 : 9811623732
Total Pages : 179 pages
Book Rating : 4.8/5 (116 download)
Download or read book Scattering Theory for Transport Phenomena written by Hassan Emamirad and published by Springer Nature. This book was released on 2021-06-27 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten–von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland’s formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schrödinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.
Author : Peter D. Lax
Publisher : Elsevier
ISBN 13 : 1483223639
Total Pages : 289 pages
Book Rating : 4.4/5 (832 download)
Download or read book Scattering Theory written by Peter D. Lax and published by Elsevier. This book was released on 2016-06-03 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering Theory describes classical scattering theory in contrast to quantum mechanical scattering theory. The book discusses the formulation of the scattering theory in terms of the representation theory. The text also explains the relation between the behavior of the solution of the perturbed problem at small distances for large positive times and the analytic continuation of the scattering matrix. To prove the representation theorem, the text cites the methods used by Masani and Robertson in their work dealing with stationary stochastic processes. The book also applies the translation representation theory to a wave equation to obtain a comparison of the asymptotic properties of the free space solution with those of the solution in an exterior domain. The text discusses the solution of the wave equation in an exterior domain by fitting this problem into the abstract framework to get a verification of the hypotheses in some other theorems. The general theory of scattering can be applied to symmetric hyperbolic systems in which all sound speeds are different from zero, as well as to the acoustic equation which has a potential that can cause an energy form to become indefinite. The book is suitable for proponents of analytical mathematics, particle physics, and quantum physics.
Author : Dmitri R. Yafaev
Publisher : Springer
ISBN 13 : 3540451706
Total Pages : 185 pages
Book Rating : 4.5/5 (44 download)
Download or read book Scattering Theory: Some Old and New Problems written by Dmitri R. Yafaev and published by Springer. This book was released on 2007-05-06 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Author : Cathleen S. Morawetz
Publisher : SIAM
ISBN 13 : 0898710162
Total Pages : 84 pages
Book Rating : 4.8/5 (987 download)
Download or read book Notes on Time Decay and Scattering for Some Hyperbolic Problems written by Cathleen S. Morawetz and published by SIAM. This book was released on 1975-06-01 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions of the wave equation or Maxwell's equations in boundary value and free space problems are analyzed. Hyperbolic systems in domains going off to infinity are studied. New results on Maxwell's equations and non-star shaped reflecting bodies are included.
Author : Baumgärtel
Publisher : Birkhäuser
ISBN 13 : 3034854404
Total Pages : 448 pages
Book Rating : 4.0/5 (348 download)
Download or read book Mathematical Scattering Theory written by Baumgärtel and published by Birkhäuser. This book was released on 2013-12-11 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering Theory within the framework of operator theory in Hilbert space. The term Mathematical Scattering Theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operator theory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering Theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.
Author : D. R. Yafaev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897379
Total Pages : 356 pages
Book Rating : 4.8/5 (973 download)
Download or read book Mathematical Scattering Theory written by D. R. Yafaev and published by American Mathematical Soc.. This book was released on 1992-09-09 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preliminary facts Basic concepts of scattering theory Further properties of the WO Scattering for relatively smooth perturbations The general setup in stationary scattering theory Scattering for perturbations of trace class type Properties of the scattering matrix (SM) The spectral shift function (SSF) and the trace formula
Author : H. Baumgärtel
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112707818
Total Pages : 452 pages
Book Rating : 4.1/5 (127 download)
Download or read book Mathematical Scattering Theory written by H. Baumgärtel and published by Walter de Gruyter GmbH & Co KG. This book was released on 1983-12-31 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keine ausführliche Beschreibung für "Mathematical Scattering Theory" verfügbar.
Author : Richard B. Melrose
Publisher : Cambridge University Press
ISBN 13 : 9780521498104
Total Pages : 134 pages
Book Rating : 4.4/5 (981 download)
Download or read book Geometric Scattering Theory written by Richard B. Melrose and published by Cambridge University Press. This book was released on 1995-07-28 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as a non-technical overview of scattering theory.
Author : Hiroshi Isozaki
Publisher : Springer Nature
ISBN 13 : 9811581991
Total Pages : 130 pages
Book Rating : 4.8/5 (115 download)
Download or read book Inverse Spectral and Scattering Theory written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2020-09-26 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
