LEADER 06724nam 22017055 450 001 9910154746703321 005 20190708092533.0 010 $a1-4008-8156-0 024 7 $a10.1515/9781400881567 035 $a(CKB)3710000000627793 035 $a(MiAaPQ)EBC4738530 035 $a(DE-B1597)468001 035 $a(OCoLC)979836504 035 $a(DE-B1597)9781400881567 035 $a(EXLCZ)993710000000627793 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aScattering Theory for Automorphic Functions. (AM-87), Volume 87 /$fPeter D. Lax, Ralph S. Phillips 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1977 215 $a1 online resource (313 pages) 225 0 $aAnnals of Mathematics Studies ;$v257 311 $a0-691-08184-0 311 $a0-691-08179-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tTABLE OF CONTENTS -- $tPREFACE -- $tLIST OF SYMBOLS -- $t§1. INTRODUCTION -- $t§2. AN ABSTRACT SCATTERING THEORY -- $t§3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM -- $t§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP -- $t§5. THE AUTOMORPHIC WAVE EQUATIONS -- $t§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION -- $t§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION -- $t§8. THE GENERAL CASE -- $t§9. THE SELBERG TRACE FORMULA -- $tREFERENCES -- $tINDEX -- $tBackmatter 330 $aThe application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula.CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula. 410 0$aAnnals of mathematics studies ;$vNumber 87. 606 $aAutomorphic functions 606 $aScattering (Mathematics) 610 $aAbsolute continuity. 610 $aAlgebra. 610 $aAnalytic continuation. 610 $aAnalytic function. 610 $aAnnulus (mathematics). 610 $aAsymptotic distribution. 610 $aAutomorphic function. 610 $aBilinear form. 610 $aBoundary (topology). 610 $aBoundary value problem. 610 $aBounded operator. 610 $aCalculation. 610 $aCauchy sequence. 610 $aChange of variables. 610 $aComplex plane. 610 $aConjugacy class. 610 $aConvolution. 610 $aCusp neighborhood. 610 $aCyclic group. 610 $aDerivative. 610 $aDifferential equation. 610 $aDifferential operator. 610 $aDimension (vector space). 610 $aDimensional analysis. 610 $aDirichlet integral. 610 $aDirichlet series. 610 $aEigenfunction. 610 $aEigenvalues and eigenvectors. 610 $aEisenstein series. 610 $aElliptic operator. 610 $aElliptic partial differential equation. 610 $aEquation. 610 $aEquivalence class. 610 $aEven and odd functions. 610 $aExistential quantification. 610 $aExplicit formula. 610 $aExplicit formulae (L-function). 610 $aExponential function. 610 $aFourier transform. 610 $aFunction space. 610 $aFunctional analysis. 610 $aFunctional calculus. 610 $aFundamental domain. 610 $aHarmonic analysis. 610 $aHilbert space. 610 $aHyperbolic partial differential equation. 610 $aInfinitesimal generator (stochastic processes). 610 $aIntegral equation. 610 $aIntegration by parts. 610 $aInvariant subspace. 610 $aLaplace operator. 610 $aLaplace transform. 610 $aLebesgue measure. 610 $aLinear differential equation. 610 $aLinear space (geometry). 610 $aMatrix (mathematics). 610 $aMaximum principle. 610 $aMeromorphic function. 610 $aModular group. 610 $aNeumann boundary condition. 610 $aNorm (mathematics). 610 $aNull vector. 610 $aNumber theory. 610 $aOperator theory. 610 $aOrthogonal complement. 610 $aOrthonormal basis. 610 $aPaley?Wiener theorem. 610 $aPartial differential equation. 610 $aPerturbation theory (quantum mechanics). 610 $aPerturbation theory. 610 $aPrimitive element (finite field). 610 $aPrincipal component analysis. 610 $aProjection (linear algebra). 610 $aQuadratic form. 610 $aRemovable singularity. 610 $aRepresentation theorem. 610 $aResolvent set. 610 $aRiemann hypothesis. 610 $aRiemann surface. 610 $aRiemann zeta function. 610 $aRiesz representation theorem. 610 $aScatter matrix. 610 $aScattering theory. 610 $aSchwarz reflection principle. 610 $aSelberg trace formula. 610 $aSelf-adjoint. 610 $aSemigroup. 610 $aSign (mathematics). 610 $aSpectral theory. 610 $aSubgroup. 610 $aSubsequence. 610 $aSummation. 610 $aSupport (mathematics). 610 $aTheorem. 610 $aTrace class. 610 $aTrace formula. 610 $aUnitary operator. 610 $aWave equation. 610 $aWeighted arithmetic mean. 610 $aWinding number. 615 0$aAutomorphic functions. 615 0$aScattering (Mathematics) 676 $a515.9 700 $aLax$b Peter D., $042253 702 $aPhillips$b Ralph S., 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154746703321 996 $aScattering Theory for Automorphic Functions. (AM-87), Volume 87$92788031 997 $aUNINA