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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spectral theory of the linearized Vlasov-Poisson equation
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by Pierre Degond PDF
Trans. Amer. Math. Soc. 294 (1986), 435-453 Request permission


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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 435-453
  • MSC: Primary 35P05; Secondary 35Q20, 76X05, 82A45
  • DOI:
  • MathSciNet review: 825714