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Displaying 361 –
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The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of gn. Moreover, we give a procedure to obtain abelian Lie subalgebras of gn up to the dimension which we think it is the maximum.
We study the problem of -boundedness () of operators of the form for a commuting system of self-adjoint left-invariant differential operators on a Lie group of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when is a homogeneous group and are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.
The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov.
In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.
We generalize to the non-separable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a joint-continuity result for non-separable normed groups, previously known only in the separable context.
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