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
MathSciNet review:
4163830
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
Keywords:
Beurling–Björck 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
