On montre, pour une classe particulière de groupes non-unimodulaires , où est un groupe de Lie stratifié et où l’action de est définie par les dilatations naturelles de , et pour les sous-laplaciens invariants à gauche correspondants , que toute fonction possédant un support compact dans définit un opérateur borné sur les espaces de Lebesgue associés à la mesure de Haar invariante à droite sur , .
We define a category containing the discrete quantum groups (and hence the discrete groups and the duals of compact groups) and the compact quantum groups (and hence the compact groups and the duals of discrete groups). The dual of an object can be defined within the same category and we have a biduality theorem. This theory extends the duality between compact quantum groups and discrete quantum groups (and hence the one between compact abelian groups and discrete abelian groups). The objects in...
A multiresolution analysis is defined in a class of locally compact abelian groups . It is shown that the spaces of integrable functions and the complex Radon measures admit a simple characterization in terms of this multiresolution analysis.
[For the entire collection see Zbl 0742.00067.]This paper is devoted to a method permitting to determine explicitly all multilinear natural operators between vector-valued differential forms and between sections of several other natural vector bundles.