Dispersion decay and scattering theory / / Alexander Komech, Elena Kopylova

• Autore: Komech A. I
• Pubblicazione: Hoboken, N.J., : Wiley, c2012
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (204 p.)
• Disciplina: 530.12/4
• Soggetto topico: Klein-Gordon equation; Spectral theory (Mathematics); Scattering (Mathematics)
• Altri autori: KopylovaElena <1960->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 equation ; 7.1 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 transform ; 11.2 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 resolvent ; 19.1 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 operator ; 25 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 equation ; 40.1 Spectral properties
• Sommario/riassunto: A 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 p
• Titolo autorizzato: Dispersion decay and scattering theory
• ISBN: 1-282-16526-7; 9786613808523; 1-118-38288-9; 1-118-38289-7; 1-118-38286-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818851903321
• Lo trovi qui: Univ. Federico II