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arXiv · 1902.09187

About the nuclearity of ${\mathcal S}_{(M_{p})}$ and ${\mathcal S}_{\omega}$

Chiara Boiti·David Jornet·Alessandro Oliaro
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Abstract

We use an isomorphism established by Langenbruch between some sequence spaces and weighted spaces of generalized functions to give sufficient conditions for the (Beurling type) space ${\mathcal S}_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $\omega$ satisfying the mild condition: $2\omega(t)\leq \omega(Ht)+H$ for some $H>1$ and for all $t\geq0$, the space ${\mathcal S}_\omega$ in the sense of Bj\"orck is also nuclear.

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Chiara Boiti, David Jornet, Alessandro Oliaro. 2019-02-25. About the nuclearity of ${\mathcal S}_{(M_{p})}$ and ${\mathcal S}_{\omega}$. https://doi.org/10.1007/978-3-030-36138-9_6

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