  We are interested in the inhomogeneous Landau equation which describes the
evolution of a particle density f = f (t, x, v) representing at time t $\ge$ 0,
the density of particles at position x $\in$ R 3 and velocity v $\in$ R 3. The
study is motivated by the linearization of the Landau equation near Maxwellian
distribution. In this article, we establish hypoelliptic estimates, a
localization of the spectrum and estimates of the resolvent of the linear
Landau operator with hard potentials and Maxwellian molecules. The proof is
based on a multiplier method and requires fine pseudo-differential calculus
tools.
