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arXiv · 1906.05171

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

Chiara Boiti·David Jornet·Alessandro Oliaro·Gerhard Schindl
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Abstract

We use techniques from time-frequency analysis to show that the space $\mathcal S_ω$ 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 $(M_p)_p$ 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.

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Chiara Boiti, David Jornet, Alessandro Oliaro, Gerhard Schindl. 2019-06-12. Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis. https://doi.org/10.1007/s13348-020-00296-0

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