Eigenspaces of Invariant Differential Operators on an Affine Symmetric Space.
We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on .
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.