Semicharacters and Solvable Lie Croups.
Semigroups in lattices of solvable Lie groups.
Separation of unitary representations of .
Sharp Inequalities for Weyl Operators and Heisenberg Groups.
Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups
Some oscillatory integrals and their applications
Some properties of Carnot-Carathéodory balls in the Heisenberg group
Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. in the classical sense for all with , where is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.
Special Functions and Infinite-dimensional Representations of Lie Groups.
Spectral multipliers on metabelian groups.
Let G be a Lie group, Xj right invariant vector fields on G, which generate (as a Lie algebra) the Lie algebra of G,L = -Σ Xj2.(...) In this paper we consider L1(G) boundedness of F(L) for (some) metabelian G and a distinguished L on G. Of the main interest is that the group is of exponential growth, and possibly higher rank. Previously positive results about higher rank groups were only about Iwasawa type groups. Also, our groups may be unimodular, so it is the second positive result (after [13])...
Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.
The aim of this paper is to study mean value operators on the reduced Heisenberg group Hn/Γ, where Hn is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of Hn.
Square-integrable representations mod of unipotent groups
Stein Quotients of Connected Complex Lie Groups.
Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group
We prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian.
Sub-Laplacian with drift in nilpotent Lie groups
We consider the heat kernel corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for . We also obtain a large time lower Gaussian estimate for .
Sums of adjoint orbits.
Superrigidity of lattices in solvable Lie groups.
Sur les feuilletages induits par l'action de groupes de Lie nilpotents
Nous étudions ici les feuilletages de codimension un induits par les actions non dégénérées de groupes nilpotents.L’existence de feuilles non compactes isolées d’un côté, implique celle d’idéaux remarquables dans l’algèbre de Lie du groupe.Dans la deuxième partie, nous montrons, dans le cas des groupes de Heisenberg des théorèmes de fibration et de cobordisme généralisant ceux obtenus par H. Rosenberg et l’auteur pour (cf. Cahiers IHES, 1974).
Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional.
Symplectic structures and cohomologies on some solvmanifolds.
Symplectic torus actions with coisotropic principal orbits
In this paper we completely classify symplectic actions of a torus on a compact connected symplectic manifold when some, hence every, principal orbit is a coisotropic submanifold of . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...