Dual topology of diamond groups.
A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
Inspiré par un travail de J.-P. Bézivin et F. Gramain sur les systèmes d’équations aux différences, on caractérise les sous-groupes d’un groupe de Lie réel (resp. complexe) , pour lesquels toute fonction continue (resp. entière) telle que l’ensemble des -translatées engendrent un -espace vectoriel de dimension finie, engendrent aussi un -espace vectoriel de dimension finie par - translation. On fait le lien avec les systèmes d’équations aux différences à coefficients constants.
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
This is a short description of some results obtained by Ewa Damek, Andrzej Hulanicki, Richard Penney and Jacek Zienkiewicz. They belong to harmonic analysis on a class of solvable Lie groups called NA. We apply our results to analysis on classical Siegel domains.
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.
The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.
Nous donnons des exemples de feuilletages de Lie sur une variété compacte qui ne se déforment pas en des feuilletages de Lie à holonomie discrète.
Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.