  The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.
