On 3-symmetric Riemannian spaces of solvable type
We study the densities of the semigroup generated by the operator on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are . We give explicit spectral decomposition of images of in representations.
In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.
For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.