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An obstruction to represent abelian Lie algebras by unipotent matrices.

J. C. Benjumea, F. J. Echarte, Núñez, J.,Tenorio, A. F. (2004)

Extracta Mathematicae

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.

Analysis of joint spectral multipliers on Lie groups of polynomial growth

Alessio Martini (2012)

Annales de l’institut Fourier

We study the problem of L p -boundedness ( 1 < p < ) of operators of the form m ( L 1 , , L n ) for a commuting system of self-adjoint left-invariant differential operators L 1 , , L n on a Lie group G of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when G is a homogeneous group and L 1 , , L n are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.

Analysis on Extended Heisenberg Group

B. Zegarliński (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.

Analytic Baire spaces

A. J. Ostaszewski (2012)

Fundamenta Mathematicae

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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