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.
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