Plasma oscillations

For a simple model of a linearized plasma the normal modes are discussed for the case when an n fold degenerate eigenvalue is imbedded in the continuum. It is found that for each such eigenvalue there are 2n generalized eigenfunctions and 2n adjoint functions. The set consisting of the continuum modes, and discrete modes of both complex and real eigenvalues are complete. Expansions are readily found using biorthogonality relations which are obtained.