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Peter D. Lax | Ralph S. Phillips

Scattering Theory for Automorphic Functions

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€117.99
A01=Peter D. Lax
A01=Ralph S. Phillips
Analytic continuation
Analytic function
Annulus (mathematics)
Asymptotic distribution
Author_Peter D. Lax
Author_Ralph S. Phillips
Automorphic function
Boundary (topology)
Boundary value problem
Bounded operator
Category=PB
Cauchy sequence
Conjugacy class
Derivative
Differential operator
Dimension (vector space)
Dirichlet integral
Dirichlet series
Eigenfunction
Eigenvalues and eigenvectors
Eisenstein series
Elliptic operator
Elliptic partial differential equation
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Even and odd functions
Explicit formulae (L-function)
Exponential function
Fourier transform
Function space
Functional calculus
Fundamental domain
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
Meromorphic function
Modular group
Norm (mathematics)
Number theory
Operator theory
Orthonormal basis
Paley-Wiener theorem
Partial differential equation
Perturbation theory
Perturbation theory (quantum mechanics)
Primitive element (finite field)
Principal component analysis
Projection (linear algebra)
Representation theorem
Resolvent set
Riemann hypothesis
Riemann surface
Riemann zeta function
Riesz representation theorem
Scatter matrix
Scattering theory
Schwarz reflection principle
Selberg trace formula
Sign (mathematics)
Spectral theory
Subgroup
Summation
Support (mathematics)
Theorem
Trace class
Trace formula
Wave equation

Product details

  • ISBN 9780691081847
  • Weight: 454g
  • Dimensions: 152 x 229mm
  • Publication Date: 21 Jan 1977
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Paperback
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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.