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

Alessandro Oliaro;
2021-01-01

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
72
2
423
442
https://arxiv.org/abs/1906.05171
Nuclear spaces, weighted spaces of ultradifferentiable functions of Beurling type, Gabor frames, time-frequency analysis.
Chiara Boiti, David Jornet, Alessandro Oliaro, Gerhard Schindl
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1740930
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