Scattering Theory For Automorphic Functions
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Scattering Theory For Automorphic Functions
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Author : Peter D. Lax
language : en
Publisher: Princeton University Press
Release Date : 1976
Scattering Theory For Automorphic Functions written by Peter D. Lax and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula. CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.
Scattering Theory For Automorphic Functions
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Author : Peter D. Lax
language : en
Publisher:
Release Date : 1976
Scattering Theory For Automorphic Functions written by Peter D. Lax and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Scattering Theory For Automorphic Functions And Its Relation To L Functions
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Author : Ioannis N. Petridis
language : en
Publisher:
Release Date : 1992
Scattering Theory For Automorphic Functions And Its Relation To L Functions written by Ioannis N. Petridis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Scattering Theory For Automorphic Functions Am 87 Volume 87
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Author : Peter D. Lax
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Scattering Theory For Automorphic Functions Am 87 Volume 87 written by Peter D. Lax and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula. CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.
Spectral Theory Of Automorphic Functions
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Author : A. B. Venkov
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Spectral Theory Of Automorphic Functions written by A. B. Venkov 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 1983 with Mathematics categories.
Scattering Theory Revised Edition
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Author : Peter D. Lax
language : en
Publisher: Academic Press
Release Date : 1990-02-22
Scattering Theory Revised Edition written by Peter D. Lax and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-22 with Mathematics categories.
This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.
Transmutation Scattering Theory And Special Functions
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Author : R. Carroll
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Transmutation Scattering Theory And Special Functions written by R. Carroll and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Science categories.
Transmutation, Scattering Theory and Special Functions
Scattering Theory
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Author : Peter D. Lax
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Scattering Theory written by Peter D. Lax and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
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.
Mathematical Quantum Theory Ii
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Author : Joel S. Feldman
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Mathematical Quantum Theory Ii written by Joel S. Feldman 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 1995 with Science categories.
Iii Scattering Theory
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Author : Michael Reed
language : en
Publisher: Elsevier
Release Date : 1979-05-29
Iii Scattering Theory written by Michael Reed and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-05-29 with Mathematics categories.
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.