Scattering Theory for Automorphic Functions
1st Edition
Published on 20. June 2016
312 pages
978-1-4008-8156-7 (ISBN)
Description
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.
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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Peter D. Lax | Ralph S. Phillips
Scattering Theory for Automorphic Functions
Book
01/1977
Princeton University Press
€94.50
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Peter D. Lax | Ralph S. Phillips
Scattering Theory for Automorphic Functions
Book
01/1977
Princeton University Press
€55.71
Article exhausted; check different version
Persons
Peter D. Lax & Ralph S. Phillips
Content
Frontmatter, pg. i
TABLE OF CONTENTS, pg. v
PREFACE, pg. vii
LIST OF SYMBOLS, pg. ix
§1. INTRODUCTION, pg. 1
§2. AN ABSTRACT SCATTERING THEORY, pg. 12
§3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM, pg. 53
§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP, pg. 87
§5. THE AUTOMORPHIC WAVE EQUATIONS, pg. 102
§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION, pg. 119
§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION, pg. 149
§8. THE GENERAL CASE, pg. 191
§9. THE SELBERG TRACE FORMULA, pg. 220
REFERENCES, pg. 297
INDEX, pg. 299
Backmatter, pg. 301
TABLE OF CONTENTS, pg. v
PREFACE, pg. vii
LIST OF SYMBOLS, pg. ix
§1. INTRODUCTION, pg. 1
§2. AN ABSTRACT SCATTERING THEORY, pg. 12
§3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM, pg. 53
§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP, pg. 87
§5. THE AUTOMORPHIC WAVE EQUATIONS, pg. 102
§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION, pg. 119
§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION, pg. 149
§8. THE GENERAL CASE, pg. 191
§9. THE SELBERG TRACE FORMULA, pg. 220
REFERENCES, pg. 297
INDEX, pg. 299
Backmatter, pg. 301
