Ralph S. Phillips's Books

Scattering Theory, Revised Edition

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory, Revised Edition

By: Peter D. Lax,Ralph S. Phillips

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.

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Page Count

329

Publisher

Academic Press

Published Date

ISBN 10

0080873383

ISBN 13

9780080873381

Scattering Theory for Automorphic Functions. (AM-87), Volume 87

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory for Automorphic Functions. (AM-87), Volume 87

By: Peter D. Lax,Ralph S. Phillips

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.

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312

Publisher

Princeton University Press

Published Date

ISBN 10

1400881560

ISBN 13

9781400881567

Scattering Theory

Pure and Applied Mathematics, Vol. 26

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory

Pure and Applied Mathematics, Vol. 26

By: Peter D. Lax,Ralph S. Phillips

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.

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Page Count

289

Publisher

Elsevier

Published Date

ISBN 10

1483223639

ISBN 13

9781483223636

Scattering Theory for Automorphic Functions

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory for Automorphic Functions

By: Peter D. Lax,Ralph S. Phillips

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Page Count

316

Publisher

Princeton University Press

Published Date

ISBN 10

0691081840

ISBN 13

9780691081847

Book's by Ralph S. Phillips

Scattering Theory, Revised Edition

Scattering Theory, Revised Edition

Scattering Theory for Automorphic Functions. (AM-87), Volume 87

Scattering Theory for Automorphic Functions. (AM-87), Volume 87

Scattering Theory

Scattering Theory

Scattering Theory for Automorphic Functions

Scattering Theory for Automorphic Functions

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