Virginia TechArthur, Michael D.Greenberg, WilliamZweifel, Paul F.2014-04-242014-04-241977Arthur, M. D.; Greenberg, W.; Zweifel, P. F., "Vlasov theory of plasma oscillations: linear-approximation," Phys. Fluids 20, 1296 (1977); http://dx.doi.org/10.1063/1.8620001070-6631http://hdl.handle.net/10919/47672A functional analytic approach to the linearized collisionless Vlasov equation is presented utilizing a resolvent integration technique on the resolvent of the transport operator evaluated at a particular point. Formulae for the eigenfunction expansion are found for cases in which the plasma disperion function _ has first and second order zeroes. Special care is taken in the study of real zeroes of _ culminating in new results for this case. For a simple zero of _ with nonvanishing imaginary part the van Kampen-Case discrete modes are reproduced. The results are used to obtain the solution to the initial value problem.en-USIn CopyrightArticle - RefereedAIP Publishinghttp://scitation.aip.org/content/aip/journal/pof1/20/8/10.1063/1.862000https://doi.org/10.1063/1.862000