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

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

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    Bog E-bog
    • Format
    • Bog, paperback
    • Engelsk

    Beskrivelse

    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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    Equation Operator theory Spectral theory Eisenstein series Number theory Dirichlet series Riemann hypothesis Wave equation Hilbert space Selberg trace formula Scattering theory Bounded operator Analytic function Functional Calculus Boundary value problem Linear differential equation Riemann surface Modular group Exponential function Lebesgue measure Trace Formula Eigenvalues and Eigenvectors Perturbation theory Theorem Laplace-Operator Derivative Function space Principal component analysis Hyperbolic partial differential equation Elliptic operator Riemann zeta function Meromorphic function Analytic Continuation Fourier transform Integral equation Partial differential equation Cauchy Sequence Paley-Wiener theorem Invariant subspace Riesz representation theorem Orthonormal basis Asymptotic distribution Integration by parts Eigenfunction Laplace-Transform Conjugacy Class Annulus (mathematics) Boundary (topology) Automorphic Function Dimension (vector space) Even and odd functions differential operator Dirichlet integral Elliptic partial differential equation Explicit formulae (L-function) Norm (mathematics) Fundamental Domain Perturbation theory (quantum mechanics) Infinitesimal generator (stochastic processes) Representation theorem Schwarz reflection principle Resolvent Set Sign (mathematics) subgroup summation Support (mathematics) Projection (linear algebra) Trace class Scatter matrix Primitive element (finite field)
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