Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Spectral theory of the linearized Vlasov-Poisson equation
HTML articles powered by AMS MathViewer

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.
    N. A. Krall and A. W. Trivelpiece, Principles of plasma physics, McGraw-Hill, New York, 1973.
  • Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • P. Degond, Existence et comportement asymptotique des solutions de l’équation de Vlasov-Poisson linéarisée, Thèse de 3ème cycle, Univ. P. & M. Curie, 1983.
  • Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • N. I. Muskhelishvilli, Singular integral equations, Noordhoff, Groningen, 1977. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Univ., 1937.
  • N. G. van Kampen, On the theory of stationary waves in plasmas, Physica 21 (1955), 949–963. MR 75080
  • K. M. Case, Plasma oscillations, Ann. Physics 7 (1959), 349–364. MR 106007, DOI 10.1016/0003-4916(59)90029-6
  • M. Trocheris, Sur les modes normaux des oscillations de plasma, Fusion Nucléaire 5 (1965).
Similar Articles
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