Dispersion Decay and Scattering Theory

A simplified, yet rigorous treatment of scattering theorymethods and their applications

Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theorymethods to modern problems in mathematics, quantum physics, andmathematical physics. Introducing spectral methods withapplications to dispersion time-decay and scattering theory, thisbook presents, for the first time, the Agmon-Jensen-Kato spectraltheory for the Schr?dinger equation, extending the theory to theKlein-Gordon equation. The dispersion decay plays a crucial role inthe modern application to asymptotic stability of solitons ofnonlinear Schr?dinger and Klein-Gordon equations.

The authors clearly explain the fundamental concepts andformulas of the Schr?dinger operators, discuss the basic propertiesof the Schr?dinger equation, and offer in-depth coverage ofAgmon-Jensen-Kato theory of the dispersion decay in the weightedSobolev norms. The book also details the application of dispersiondecay to scattering and spectral theories, the scattering crosssection, and the weighted energy decay for 3D Klein-Gordon and waveequations. Complete streamlined proofs for key areas of theAgmon-Jensen-Kato approach, such as the high-energy decay of theresolvent and the limiting absorption principle are alsoincluded.

Dispersion Decay and Scattering Theory is a suitable bookfor courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also servesas an excellent resource for researchers, professionals, andacademics in the fields of mathematics, mathematical physics, andquantum physics who would like to better understand scatteringtheory and partial differential equations and gain problem-solvingskills in diverse areas, from high-energy physics to wavepropagation and hydrodynamics.