Harmonische Analyse auf gewissen nilpotenten Lieschen Gruppen
Heat kernel estimates for a class of higher order operators on Lie groups
Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates....
Heat kernels and Riesz transforms on nilpotent Lie groups
We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds...
Hodge numbers and invariant complex structures of compact nilmanifolds
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces
We prove that Huygens’ principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek–Ricci spaces. We also prove a Paley–Wiener type theorem for the inverse of the Helgason Fourier transform on Damek–Ricci spaces.
Hypoellipticité analytique sur des groupes nilpotents de rang 2 (d'après G. Metivier)
Hypoellipticité pour des groupes nilpotents de rang de nilpotence
Hypoellipticité pour des opérateurs différentiels sur des groupes de Lie nilpotents