The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology σ(X, X ) of a locally convex space ...

[EN] We use techniques from time-frequency analysis to show that the space S(omega )of rapidly decreasing omega-ultradifferentiable functions is nuclear for every weight function omega(t) = o(t) as t tends to infinity. ...