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.

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

Chiara Boiti
Primo
;
2021

Abstract

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.
2021
Boiti, Chiara; Jornet, David; Oliaro, Alessandro; Schindl, Gerhard
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2405102
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