Topological properties of convolutor spaces via the short-time Fourier transform
Authors:
Andreas Debrouwere and Jasson Vindas
Journal:
Trans. Amer. Math. Soc. 374 (2021), 829-861
MSC (2010):
Primary 46A13, 46E10, 46F05; Secondary 46M18, 81S30
DOI:
https://doi.org/10.1090/tran/8080
Published electronically:
November 18, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We discuss the structural and topological properties of a general class of weighted convolutor spaces. Our theory simultaneously applies to weighted
spaces as well as to convolutor spaces of the Gelfand-Shilov spaces
. In particular, we characterize the sequences of weight functions
for which the space of convolutors of
is ultrabornological, thereby generalizing Grothendieck's classical result for the space
of rapidly decreasing distributions. Our methods lead to the first direct proof of the completeness of the space
of very slowly increasing smooth functions.
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Additional Information
Andreas Debrouwere
Affiliation:
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
Email:
andreas.debrouwere@ugent.be
Jasson Vindas
Affiliation:
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
Email:
jasson.vindas@ugent.be
DOI:
https://doi.org/10.1090/tran/8080
Keywords:
Convolutor spaces,
short-time Fourier transform,
completeness of inductive limits,
Gelfand-Shilov spaces
Received by editor(s):
September 21, 2018
Received by editor(s) in revised form:
June 8, 2019, and November 21, 2019
Published electronically:
November 18, 2020
Additional Notes:
The first author was supported by FWO-Vlaanderen through the postdoctoral grant 12T0519N
The second author was supported by Ghent University through the BOF-grants 01J11615 and 01J04017.
Article copyright:
© Copyright 2020
American Mathematical Society