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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Spectral theory of the linearized Vlasov-Poisson equation

Author: Pierre Degond
Journal: Trans. Amer. Math. Soc. 294 (1986), 435-453
MSC: Primary 35P05; Secondary 35Q20, 76X05, 82A45
MathSciNet review: 825714
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Abstract: We study the spectral theory of the linearized Vlasov-Poisson 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.

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Article copyright: © Copyright 1986 American Mathematical Society