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Characterization of nuclearity for Beurling-Björck spaces


Authors: Andreas Debrouwere, Lenny Neyt and Jasson Vindas
Journal: Proc. Amer. Math. Soc. 148 (2020), 5171-5180
MSC (2010): Primary 46E10, 46F05; Secondary 42B10, 46A11, 81S30
DOI: https://doi.org/10.1090/proc/15227
Published electronically: September 18, 2020
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Abstract: We characterize the nuclearity of the Beurling-Björck spaces
$ \mathcal {S}^{(\omega )}_{(\eta )}(\mathbb{R}^d)$ and $ \mathcal {S}^{\{\omega \}}_{\{\eta \}}(\mathbb{R}^d)$ in terms of the defining weight functions $ \omega $ and $ \eta $.


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Additional Information

Andreas Debrouwere
Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
MR Author ID: 1154620
Email: andreas.debrouwere@UGent.be

Lenny Neyt
Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
MR Author ID: 1337474
ORCID: 0000-0001-8116-1487
Email: lenny.neyt@UGent.be

Jasson Vindas
Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
MR Author ID: 795097
ORCID: 0000-0002-3789-8577
Email: jasson.vindas@UGent.be

DOI: https://doi.org/10.1090/proc/15227
Keywords: Beurling--Bj\"orck spaces, nuclear spaces, ultradifferentiable functions, the short-time Fourier transform, time-frequency analysis methods in functional analysis
Received by editor(s): August 28, 2019
Received by editor(s) in revised form: February 15, 2020
Published electronically: September 18, 2020
Additional Notes: The first author was supported by FWO-Vlaanderen through the postdoctoral grant 12T0519N
The second author gratefully acknowledges support by Ghent University through the BOF-grant 01J11615.
The third author was supported by Ghent University through the BOF-grants 01J11615 and 01J04017.
Communicated by: Ariel Barton
Article copyright: © Copyright 2020 American Mathematical Society