Spectral theory of the linearized VlasovPoisson equation
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 by Pierre Degond PDF
 Trans. Amer. Math. Soc. 294 (1986), 435453 Request permission
Abstract:
We study the spectral theory of the linearized VlasovPoisson equation, in order to prove that its solution behaves, for large times, like a sum of plane waves. To obtain such an expansion involving damped waves, we must find an analytical extension of the resolvent of the equation. Then, the poles of this extension are no longer eigenvalues and must be interpreted as eigenmodes, associated to “generalized eigenfunctions” which actually are linear functionals on a Banach space of analytic functions.References

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Additional Information
 © Copyright 1986 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 294 (1986), 435453
 MSC: Primary 35P05; Secondary 35Q20, 76X05, 82A45
 DOI: https://doi.org/10.1090/S00029947198608257148
 MathSciNet review: 825714