Abstract:Abstract. We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensi… Show more
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