دانلود کتاب Dispersion Decay and Scattering Theory – نظریه پوسیدگی پراکندگی و پراکندگی

توضیحات

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 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.Content:
Chapter 1 Basic Concepts and Formulas (pages 19):
Chapter 2 Nonstationary Schrodinger Equation (pages 1124):
Chapter 3 Stationary Schrodinger Equation (pages 2536):
Chapter 4 Spectral Theory (pages 3757):
Chapter 5 High Energy Decay of Resolvent (pages 5969):
Chapter 6 Limiting Absorption Principle (pages 7188):
Chapter 7 Dispersion Decay (pages 8995):
Chapter 8 Scattering Theory and Spectral Resolution (pages 97109):
Chapter 9 Scattering Cross Section (pages 111131):
Chapter 10 Klein?Gordon Equation (pages 133150):
Chapter 11 Wave Equation (pages 151166):

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ترجمه ماشینی :

یک درمان ساده و در عین حال دقیق از روشهای تئوری پراکندگی و کاربردهای آنها

پوسیدگی پراکندگی و تئوری پراکندگی راهنمایی در مورد استفاده از روشهای تئوری پراکندگی به مشکلات مدرن در ریاضیات ، فیزیک کوانتومی و فیزیک ریاضی. این کتاب با معرفی روش های طیفی با برنامه های کاربردی برای پراکندگی زمان و پراکندگی نظریه ، برای اولین بار تئوری طیفی Agmon-Jensen-Kato را برای معادله Schr؟ Dinger ارائه می دهد و این تئوری را به معادله Klein-Gordon گسترش می دهد. پوسیدگی پراکندگی نقش مهمی در کاربرد مدرن برای پایداری بدون علامت از سولیتون های معادلات غیرخطی Schr؟ Dinger و Klein-Gordon دارد.