Resumen de Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

Chiara Boiti, David Jornet Casanova , Alessandro Oliaro , Gerhard Schindl

• We use techniques from time-frequency analysis to show that the space {\mathcal{S}}_\omega of rapidly decreasing \omega-ultradifferentiable functions is nuclear for every weight function \omega (t)=o(t) as t tends to infinity. Moreover, we prove that, for a sequence (M_p)_p satisfying the classical condition (M1) of Komatsu, the space of Beurling type {\mathcal{S}}_{(M_p)} when defined with L^{2} norms is nuclear exactly when condition (M2)' of Komatsu holds.