Invariant local Dirichlet forms on locally compact groups
Let \(G\) be a locally compact connected locally connected metric group (typically infinite-dimen\-sional). The authors prove the existence of Gaussian (symmetric) convolution semigroups of measures \((\mu_t)_{t>0}\) on \(G\) such that \(\mu_t\) is absolutely continuous with respect to \(\nu_{\text{r}}\) (resp. \(\nu_{\text{l}}\)), the right (resp. left) invariant Haar measure. To do this, the authors use the projective structure and the local Dirichlet spaces on \(L^2(G)\). Moreover, estimations for the associated continuous densities are obtained.
infinite-dimensional locally compact group
scientific article; zbMATH DE number 2074270
scientific article