Leseprobe
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Scattering Theory for Automorphic Functions. (AM-87), Volume 87
Ralph S. Phillips, Peter D. Lax
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Fundamental domain, Bounded operator, Riemann hypothesis, Primitive element (finite field), Projection (linear algebra), Representation theorem, Number theory, Laplace operator, Integration by parts, Eigenvalues and eigenvectors, Riemann zeta function, Integral equation, Linear differential equation, Selberg trace formula, Laplace transform, Differential operator, Equation, Operator theory, Analytic continuation, Cauchy sequence, Dimension (vector space), Boundary (topology), Asymptotic distribution, Hyperbolic partial differential equation, Elliptic partial differential equation, Riesz representation theorem, Explicit formulae (L-function), Trace class, Norm (mathematics), Summation, Eigenfunction, Lebesgue measure, Automorphic function, Derivative, Infinitesimal generator (stochastic processes), Scattering theory, Elliptic operator, Resolvent set, Spectral theory, Partial differential equation, Support (mathematics), Meromorphic function, Scatter matrix, Conjugacy class, Function space, Schwarz reflection principle, Exponential function, Perturbation theory, Theorem, Wave equation, Modular group, Fourier transform, Subgroup, Riemann surface, Orthonormal basis, Principal component analysis, Sign (mathematics), Functional calculus, Eisenstein series, Even and odd functions, Dirichlet series, Trace formula, Dirichlet integral, Boundary value problem, Annulus (mathematics), Hilbert space, Perturbation theory (quantum mechanics), Invariant subspace, Paley–Wiener theorem, Analytic function