LEADER 05497nam 2200709 a 450 001 9910818851903321 005 20240516134329.0 010 $a1-282-16526-7 010 $a9786613808523 010 $a1-118-38288-9 010 $a1-118-38289-7 010 $a1-118-38286-2 035 $a(CKB)2550000000108178 035 $a(EBL)875874 035 $a(OCoLC)804863085 035 $a(SSID)ssj0000695305 035 $a(PQKBManifestationID)11421552 035 $a(PQKBTitleCode)TC0000695305 035 $a(PQKBWorkID)10671734 035 $a(PQKB)11285906 035 $a(MiAaPQ)EBC875874 035 $a(Au-PeEL)EBL875874 035 $a(CaPaEBR)ebr10582580 035 $a(CaONFJC)MIL380852 035 $a(PPN)250668912 035 $a(EXLCZ)992550000000108178 100 $a20120330d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDispersion decay and scattering theory /$fAlexander Komech, Elena Kopylova 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$dc2012 215 $a1 online resource (204 p.) 300 $aDescription based upon print version of record. 311 $a1-118-34182-1 320 $aIncludes bibliographical references and index. 327 $aDispersion 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 Schro?dinger operator; 5.1 A priori estimate; 5.2 Hermitian symmetry; 6 Dynamics for free Schro?dinger equation; 7 Perturbed Schro?dinger equation 327 $a7.1 Reduction to integral equation7.2 Contraction mapping; 7.3 Unitarity and energy conservation; 8 Wave and scattering operators; 8.1 Mo?ller wave operators: Cook method; 8.2 Scattering operator; 8.3 Intertwining identities; 3 Stationary Schro?dinger 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 327 $a11.2 Stationary Schro?dinger 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 327 $a19.1 The case ? > 019.2 The case ? = 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 Schro?dinger operator; 24.2 Diagonalization of scattering operator 327 $a25 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 327 $a40.1 Spectral properties 330 $aA 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 606 $aKlein-Gordon equation 606 $aSpectral theory (Mathematics) 606 $aScattering (Mathematics) 615 0$aKlein-Gordon equation. 615 0$aSpectral theory (Mathematics) 615 0$aScattering (Mathematics) 676 $a530.12/4 700 $aKomech$b A. I$054215 701 $aKopylova$b Elena$f1960-$01618769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818851903321 996 $aDispersion decay and scattering theory$93950670 997 $aUNINA