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Long-Time Decay for the Linearized System of a Charged Particle in the Klein-Gordon Field

Commun. Math. Anal.
Volume 14, Number 2 (2013), 13 - 24

Long-Time Decay for the Linearized System of a Charged Particle in the Klein-Gordon Field

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Abstract

We establish a long time decay for linearized dynamics of nonlinear Hamilton system which describes interaction of a charged particle with the Klein-Gordon field. The main contribution is deriving the decay for the frozen linearized system for initial data which are symplectic orthogonal to the root space of the linear differential operator involved.