05499nam 2200697 a 450 991013887070332120200520144314.01-282-16526-797866138085231-118-38288-91-118-38289-71-118-38286-2(CKB)2550000000108178(EBL)875874(OCoLC)804863085(SSID)ssj0000695305(PQKBManifestationID)11421552(PQKBTitleCode)TC0000695305(PQKBWorkID)10671734(PQKB)11285906(MiAaPQ)EBC875874(Au-PeEL)EBL875874(CaPaEBR)ebr10582580(CaONFJC)MIL380852(PPN)250668912(EXLCZ)99255000000010817820120330d2012 uy 0engur|n|---|||||txtccrDispersion decay and scattering theory[electronic resource] /Alexander Komech, Elena KopylovaHoboken, N.J. Wileyc20121 online resource (204 p.)Description based upon print version of record.1-118-34182-1 Includes bibliographical references and index.Dispersion Decay and Scattering Theory; CONTENTS; List of Figures; Foreword; Preface; Acknowledgments; Introduction; 1 Basic Concepts and Formulas; 1 Distributions and Fourier transform; 2 Functional spaces; 2.1 Sobolev spaces; 2.2 Agmon-Sobolev weighted spaces; 2.3 Operator-valued functions; 3 Free propagator; 3.1 Fourier transform; 3.2 Gaussian integrals; 2 Nonstationary Schrodinger Equation; 4 Definition of solution; 5 Schrödinger operator; 5.1 A priori estimate; 5.2 Hermitian symmetry; 6 Dynamics for free Schrödinger equation; 7 Perturbed Schrödinger equation7.1 Reduction to integral equation7.2 Contraction mapping; 7.3 Unitarity and energy conservation; 8 Wave and scattering operators; 8.1 Möller wave operators: Cook method; 8.2 Scattering operator; 8.3 Intertwining identities; 3 Stationary Schrödinger Equation; 9 Free resolvent; 9.1 General properties; 9.2 Integral representation; 10 Perturbed resolvent; 10.1 Reduction to compact perturbation; 10.2 Fredholm Theorem; 10.3 Perturbation arguments; 10.4 Continuous spectrum; 10.5 Some improvements; 4 Spectral Theory; 11 Spectral representation; 11.1 Inversion of Fourier-Laplace transform11.2 Stationary Schrödinger equation11.3 Spectral representation; 11.4 Commutation relation; 12 Analyticity of resolvent; 13 Gohberg-Bleher theorem; 14 Meromorphic continuation of resolvent; 15 Absence of positive eigenvalues; 15.1 Decay of eigenfunctions; 15.2 Carleman estimates; 15.3 Proof of Kato Theorem; 5 High Energy Decay of Resolvent; 16 High energy decay of free resolvent; 16.1 Resolvent estimates; 16.2 Decay of free resolvent; 16.3 Decay of derivatives; 17 High energy decay of perturbed resolvent; 6 Limiting Absorption Principle; 18 Free resolvent; 19 Perturbed resolvent19.1 The case λ > 019.2 The case λ = 0; 20 Decay of eigenfunctions; 20.1 Zero trace; 20.2 Division problem; 20.3 Negative eigenvalues; 20.4 Appendix A: Sobolev Trace Theorem; 20.5 Appendix B: Sokhotsky-Plemelj formula; 7 Dispersion Decay; 21 Proof of dispersion decay; 22 Low energy asymptotics; 8 Scattering Theory and Spectral Resolution; 23 Scattering theory; 23.1 Asymptotic completeness; 23.2 Wave and scattering operators; 23.3 Intertwining and commutation relations; 24 Spectral resolution; 24.1 Spectral resolution for the Schrödinger operator; 24.2 Diagonalization of scattering operator25 T-Operator and 5-Matrix9 Scattering Cross Section; 26 Introduction; 27 Main results; 28 Limiting amplitude principle; 29 Spherical waves; 30 Plane wave limit; 31 Convergence of flux; 32 Long range asymptotics; 33 Cross section; 10 Klein-Gordon Equation; 34 Introduction; 35 Free Klein-Gordon equation; 35.1 Dispersion decay; 35.2 Spectral properties; 36 Perturbed Klein-Gordon equation; 36.1 Spectral properties; 36.2 Dispersion decay; 37 Asymptotic completeness; 11 Wave equation; 38 Introduction; 39 Free wave equation; 39.1 Time decay; 39.2 Spectral properties; 40 Perturbed wave equation40.1 Spectral propertiesA simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay pKlein-Gordon equationSpectral theory (Mathematics)Scattering (Mathematics)Klein-Gordon equation.Spectral theory (Mathematics)Scattering (Mathematics)530.12/4Komech A. I54215Kopylova Elena1960-907439MiAaPQMiAaPQMiAaPQBOOK9910138870703321Dispersion decay and scattering theory2029904UNINA