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1. |
Record Nr. |
UNICAMPANIAVAN0013037 |
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Autore |
Sitzia, Francesco |
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Titolo |
Ricerche in tema di actio aquae pluviae arcendae : dalle 12 tavole all'epoca classica / Francesco Sitzia |
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Pubbl/distr/stampa |
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Descrizione fisica |
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Disciplina |
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Soggetti |
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Actio aquae pluviae arcendae |
Diritto - Storia - Antichità |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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2. |
Record Nr. |
UNINA9910818851903321 |
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Autore |
Komech A. I |
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Titolo |
Dispersion decay and scattering theory / / Alexander Komech, Elena Kopylova |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley, c2012 |
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ISBN |
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9786613808523 |
9781282165267 |
1282165267 |
9781118382882 |
1118382889 |
9781118382899 |
1118382897 |
9781118382868 |
1118382862 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (204 p.) |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Klein-Gordon equation |
Spectral theory (Mathematics) |
Scattering (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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, |
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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 |
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