The well-known van Kampen–Case treatment of the Vlasov equation leads to a spectrum on the real axis. In this paper we show that, by going to a ‘rigged’ Hilbert space, we can derive a spectral representation that is complex and breaks time symmetry. This leads to a semigroup description in which the decay rates due to the Landau damping appear explicitly in the spectrum. Moreover, we can then define an entropy. In this way, the relation between Landau damping and irreversibility is made explicit. The analogy with the well-known Friedrichs model is stressed.