06724nam 22017055 450 991015474670332120190708092533.01-4008-8156-010.1515/9781400881567(CKB)3710000000627793(MiAaPQ)EBC4738530(DE-B1597)468001(OCoLC)979836504(DE-B1597)9781400881567(EXLCZ)99371000000062779320190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierScattering Theory for Automorphic Functions. (AM-87), Volume 87 /Peter D. Lax, Ralph S. PhillipsPrinceton, NJ : Princeton University Press, [2016]©19771 online resource (313 pages)Annals of Mathematics Studies ;2570-691-08184-0 0-691-08179-4 Includes bibliographical references and index.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 -- BackmatterThe 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.Annals of mathematics studies ;Number 87.Automorphic functionsScattering (Mathematics)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.Automorphic functions.Scattering (Mathematics)515.9Lax Peter D., 42253Phillips Ralph S., DE-B1597DE-B1597BOOK9910154746703321Scattering Theory for Automorphic Functions. (AM-87), Volume 872788031UNINA02780nam2 2200565 i 450 CFI001976420251003044110.020021105d1985 ||||0itac50 baitait11Borsa, banche e assicurazioniNapoliEdizioni scientifiche italiane1985VII, 843 p.18 cm.001FER01129042001 ˆLa ‰legislazione civile annotata con la dottrina e la giurisprudenzaa cura di Pietro Perlingieri11AssicurazioniLegislazioneFIRCFIC005790IBancheLegislazioneFIRCFIC005789IAssicurazioniLegislazioneFIRCFIC005790IBorseLegislazioneFIRCFIC005791IBancheLegislazioneFIRCFIC005789IBorseLegislazioneFIRCFIC005791I346DIRITTO PRIVATO21346Diritto privato22Contratti di assicurazioneIstituti di creditoSistemi bancariBanchi <Organizzazioni economiche>Industria bancariaContratti di assicurazioneMercati di borsaPiazze finanziarieIstituti di creditoSistemi bancariBanchi <Organizzazioni economiche>Industria bancariaMercati di borsaPiazze finanziarieAssicurazioniContratti di assicurazioneBancheIstituti di creditoBancheSistemi bancariBancheBanchi <Organizzazioni economiche>BancheIndustria bancariaAssicurazioniContratti di assicurazioneBorseMercati di borsaBorsePiazze finanziarieBancheIstituti di creditoBancheSistemi bancariBancheBanchi <Organizzazioni economiche>BancheIndustria bancariaBorseMercati di borsaBorsePiazze finanziarieITIT-00000020021105IT-BN0095 IT-NA0079 IT-BN0015 NAP BNS.MOD La consegna dei documenti è effettuata dall'Ufficio DistribuzioneCFI0019764Biblioteca Centralizzata di Ateneov. 11 in due copie 01COM (AR) DIR 346 01AR 0070013755 VMA (0011bis v. 11 (2. copia)B 2019062020190620v. 11 01COM (AR) DIR 346 01AR 0700111755 VMA (0011 v. 11B 2019061420190614v. 1-14 01POZZO LIB.ECON MON 7655 0101 0600147135E VMA (0011 v. 11 (Precedente collocazione ITA 346.45002632)B 2022081020220810 01 BN PB1.170121UNISANNIO