Research Project

Research arguments:

More precisely, our main research interests are the following:

Continuous dynamical systems. The Banach-Stone theorem for semigroups and groups of linear isometries of a Fréchet space of continuous functions. The extension from the scalar to the vector case. Wandering and non-wandering points for dynamical systems depending on a continuous parameter. Weakly and strongly periodic groups. The relations with the quasi periodic case.
Solvability for invariant differential operators on Lie groups, in particular on the Heisenberg group. Criteria for local solvability, construction of fundamental solutions.
L^p-improving property for singular measures supported on curves and asymmetry for convolution operators on non-commutative groups
Boundedness on L^p of Bergman projectors on Siegel domains of first type.
Analysis on symmetric and harmonic spaces, from Fourier analysis for vector bundles to the study of radial functions on Heisenberg-type groups and their extensions, with applications to the classification of symmetric spaces of any rank
Construction of bi-orthogonal wavelets bases on bounded domains in several dimensions and applications to the solvability of elliptic operators of second order
L^p-L^q smoothing properties and asymptotics of nonlinear parabolic differential equations, Harnack inequalities and positivity for nonlinear evolutions on manifolds on negative curvature