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

Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Ralph S. Phillips, Peter D. Lax.

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 t...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Lax, Peter D.,
Phillips, Ralph S.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1977
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 87
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spelling Lax, Peter D., author. aut http://id.loc.gov/vocabulary/relators/aut
Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / Ralph S. Phillips, Peter D. Lax.
Princeton, NJ : Princeton University Press, [2016]
©1977
1 online resource (312 p.)
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computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 87
Frontmatter -- TABLE OF CONTENTS -- PREFACE -- LIST OF SYMBOLS -- §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 EQUATIONS -- §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION -- §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION -- §8. THE GENERAL CASE -- §9. THE SELBERG TRACE FORMULA -- REFERENCES -- INDEX -- Backmatter
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Automorphic functions.
Scattering (Mathematics).
MATHEMATICS / Calculus. bisacsh
Absolute continuity.
Algebra.
Analytic continuation.
Analytic function.
Annulus (mathematics).
Asymptotic distribution.
Automorphic function.
Bilinear form.
Boundary (topology).
Boundary value problem.
Bounded operator.
Calculation.
Cauchy sequence.
Change of variables.
Complex plane.
Conjugacy class.
Convolution.
Cusp neighborhood.
Cyclic group.
Derivative.
Differential equation.
Differential operator.
Dimension (vector space).
Dimensional analysis.
Dirichlet integral.
Dirichlet series.
Eigenfunction.
Eigenvalues and eigenvectors.
Eisenstein series.
Elliptic operator.
Elliptic partial differential equation.
Equation.
Equivalence class.
Even and odd functions.
Existential quantification.
Explicit formula.
Explicit formulae (L-function).
Exponential function.
Fourier transform.
Function space.
Functional analysis.
Functional calculus.
Fundamental domain.
Harmonic analysis.
Hilbert space.
Hyperbolic partial differential equation.
Infinitesimal generator (stochastic processes).
Integral equation.
Integration by parts.
Invariant subspace.
Laplace operator.
Laplace transform.
Lebesgue measure.
Linear differential equation.
Linear space (geometry).
Matrix (mathematics).
Maximum principle.
Meromorphic function.
Modular group.
Neumann boundary condition.
Norm (mathematics).
Null vector.
Number theory.
Operator theory.
Orthogonal complement.
Orthonormal basis.
Paley-Wiener theorem.
Partial differential equation.
Perturbation theory (quantum mechanics).
Perturbation theory.
Primitive element (finite field).
Principal component analysis.
Projection (linear algebra).
Quadratic form.
Removable singularity.
Representation theorem.
Resolvent set.
Riemann hypothesis.
Riemann surface.
Riemann zeta function.
Riesz representation theorem.
Scatter matrix.
Scattering theory.
Schwarz reflection principle.
Selberg trace formula.
Self-adjoint.
Semigroup.
Sign (mathematics).
Spectral theory.
Subgroup.
Subsequence.
Summation.
Support (mathematics).
Theorem.
Trace class.
Trace formula.
Unitary operator.
Wave equation.
Weighted arithmetic mean.
Winding number.
Phillips, Ralph S., author. aut http://id.loc.gov/vocabulary/relators/aut
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691081847
https://doi.org/10.1515/9781400881567
https://www.degruyter.com/isbn/9781400881567
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language English
format eBook
author Lax, Peter D.,
Lax, Peter D.,
Phillips, Ralph S.,
spellingShingle Lax, Peter D.,
Lax, Peter D.,
Phillips, Ralph S.,
Scattering Theory for Automorphic Functions. (AM-87), Volume 87 /
Annals of Mathematics Studies ;
Frontmatter --
TABLE OF CONTENTS --
PREFACE --
LIST OF SYMBOLS --
§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 EQUATIONS --
§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION --
§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION --
§8. THE GENERAL CASE --
§9. THE SELBERG TRACE FORMULA --
REFERENCES --
INDEX --
Backmatter
author_facet Lax, Peter D.,
Lax, Peter D.,
Phillips, Ralph S.,
Phillips, Ralph S.,
Phillips, Ralph S.,
author_variant p d l pd pdl
p d l pd pdl
r s p rs rsp
author_role VerfasserIn
VerfasserIn
VerfasserIn
author2 Phillips, Ralph S.,
Phillips, Ralph S.,
author2_variant r s p rs rsp
author2_role VerfasserIn
VerfasserIn
author_sort Lax, Peter D.,
title Scattering Theory for Automorphic Functions. (AM-87), Volume 87 /
title_full Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / Ralph S. Phillips, Peter D. Lax.
title_fullStr Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / Ralph S. Phillips, Peter D. Lax.
title_full_unstemmed Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / Ralph S. Phillips, Peter D. Lax.
title_auth Scattering Theory for Automorphic Functions. (AM-87), Volume 87 /
title_alt Frontmatter --
TABLE OF CONTENTS --
PREFACE --
LIST OF SYMBOLS --
§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 EQUATIONS --
§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION --
§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION --
§8. THE GENERAL CASE --
§9. THE SELBERG TRACE FORMULA --
REFERENCES --
INDEX --
Backmatter
title_new Scattering Theory for Automorphic Functions. (AM-87), Volume 87 /
title_sort scattering theory for automorphic functions. (am-87), volume 87 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2016
physical 1 online resource (312 p.)
Issued also in print.
contents Frontmatter --
TABLE OF CONTENTS --
PREFACE --
LIST OF SYMBOLS --
§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 EQUATIONS --
§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION --
§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION --
§8. THE GENERAL CASE --
§9. THE SELBERG TRACE FORMULA --
REFERENCES --
INDEX --
Backmatter
isbn 9781400881567
9783110494914
9783110442496
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callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA353
callnumber-sort QA 3353 A9
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https://www.degruyter.com/isbn/9781400881567
https://www.degruyter.com/document/cover/isbn/9781400881567/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 515 - Analysis
dewey-full 515/.9
dewey-sort 3515 19
dewey-raw 515/.9
dewey-search 515/.9
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Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Scattering Theory for Automorphic Functions. (AM-87), Volume 87 /
container_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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