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 $CBs_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $omega$ satisfying the mild condition: $2omega(t)leq omega(Ht)+H$ for some $H>1$ and for all $tgeq0$, the space $CBs_omega$ in the sense of Bj"orck is also nuclear.

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

Alessandro Oliaro
2020

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 $CBs_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $omega$ satisfying the mild condition: $2omega(t)leq omega(Ht)+H$ for some $H>1$ and for all $tgeq0$, the space $CBs_omega$ in the sense of Bj"orck is also nuclear.
Microlocal and Time Frequency Analysis
Torino
July 2-6, 2018
Advances in Microlocal and Time-Frequency Analysis
P. Boggiatto, M. Cappiello, E. Cordero, S. Coriasco, G. Garello, A. OIiaro, J. Seiler
121
129
978-3-030-36137-2
https://arxiv.org/abs/1902.09187
https://link.springer.com/chapter/10.1007/978-3-030-36138-9_6
Nuclear spaces, weighted spaces of ultradifferentiable functions of Beurling type.
Chiara Boiti, David Jornet, Alessandro Oliaro
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1697560
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