L’opérateur de Casimir de
We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.
Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.
With an intrinsic approach on semi-simple Lie groups we find a Furstenberg–Khasminskii type formula for the limit of the diagonal component in the Iwasawa decomposition. It is an integral formula with respect to the invariant measure in the maximal flag manifold of the group (i.e. the Furstenberg boundary ). Its integrand involves the Borel type Riemannian metric in the flag manifolds. When applied to linear stochastic systems which generate a semi-simple group the formula provides a diagonal matrix...
We prove a Lyapunov type theorem for modular measures on lattice ordered effect algebras.
Let be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures have smooth densities.
Answering an open problem in [3] we show that for an even number , there exist no to mappings on the dyadic solenoid.