On the power of compact spaces
Estimates for the Poisson kernels and a Fatou type theorem applications to analysis on Siegel domains
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.
The completeness of the homeomorphisms group of a complete space
On locally compact topological groups of power of continuum
Algebraic characterization of abelian divisible groups which admit compact topologies
On the topological structure of 0-dimensional topological groups
Invariant extensions of the Lebesgue measure
A functional calculus for Rockland operators on nilpotent Lie groups
Growth of the norms of products of randomly dilated functions from A(T)
Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).
Sur les ensembles denses de puissance minimum dans les groupes topologiques
Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
Les sous-groupes purs et leurs duals
The structure of the factor group of the unrestricted sum by the restricted sum of Abelian groups II
Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains
Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone
Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators
Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II
On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups
A semi-group of probability measures with non-smooth differentiable densities on a Lie group
Asymptotic behavior of the invariant measure for a diffusion related to an NA group
On a Lie group NA that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, the heat semigroup generated by a second order subelliptic left-invariant operator is considered. Under natural conditions there is a -invariant measure m on N, i.e. . Precise asymptotics of m at infinity is given for a large class of operators with Y₀,...,Yₘ generating the Lie algebra of S.
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