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Dispersion decay and scattering theory /
"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 scatte...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
©2012.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 037 | |a 10.1002/9781118382868 |b Wiley InterScience |n http://www3.interscience.wiley.com | ||
| 050 | 4 | |a QC174.26.W28 |b K646 2012eb | |
| 072 | 7 | |a SCI |x 067000 |2 bisacsh | |
| 082 | 0 | 4 | |a 530.12/4 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Komech, A. I. | |
| 245 | 1 | 0 | |a Dispersion decay and scattering theory / |c Alexander Komech, Elena Kopylova. |
| 260 | |a Hoboken, N.J. : |b Wiley, |c ©2012. | ||
| 300 | |a 1 online resource (xxvi, 175 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |6 880-01 |a Front Matter -- Basic Concepts and Formulas -- Nonstationary Schr̲dinger Equation -- Stationary Schr̲dinger Equation -- Spectral Theory -- High Energy Decay of Resolvent -- Limiting Absorption Principle -- Dispersion Decay -- Scattering Theory and Spectral Resolution -- Scattering Cross Section -- Klein-Gordon Equation -- Wave Equation -- References -- Index. | |
| 520 | |a "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 plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics."-- |c Provided by publisher. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Klein-Gordon equation. | |
| 650 | 0 | |a Spectral theory (Mathematics) | |
| 650 | 0 | |a Scattering (Mathematics) | |
| 650 | 6 | |a Équation de Klein-Gordon. | |
| 650 | 6 | |a Spectre (Mathématiques) | |
| 650 | 6 | |a Dispersion (Mathématiques) | |
| 650 | 7 | |a SCIENCE |x Waves & Wave Mechanics. |2 bisacsh | |
| 650 | 7 | |a Klein-Gordon equation |2 fast | |
| 650 | 7 | |a Scattering (Mathematics) |2 fast | |
| 650 | 7 | |a Spectral theory (Mathematics) |2 fast | |
| 700 | 1 | |a Kopylova, Elena, |d 1960- |1 https://id.oclc.org/worldcat/entity/E39PCjM84DVKqkCq7FR3grytDq | |
| 758 | |i has work: |a Dispersion decay and scattering theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGyPDRyMvhxccBFpq9x79C |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Komech, A.I. |t Dispersion decay and scattering theory. |d Hoboken, N.J. : Wiley, ©2012 |z 9781118341827 |w (DLC) 2012007292 |w (OCoLC)777615505 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=875874 |z Texto completo |
| 880 | 8 | |6 505-01/(S |a 19.1 The case λ> 0 -- 19.2 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-Matrix -- 9 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 -- 40.2 Dispersion decay -- 41 Asymptotic completeness -- 42 Appendix: Sobolev Embedding Theorem -- References -- Index. | |
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