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 Sω of rapidly decreasing ω-ultradifferentiable functions is nuclear for every weight function ω(t)=o(t) as t tends to infinity. Moreover, we prove that, for a sequence (Mp)p satisfying the classical condition (M1) of Komatsu, the space of Beurling type S(Mp) when defined with L2 norms is nuclear exactly when condition (M2)′ of Komatsu holds.