Sequence space representations for spaces of smooth functions and distributions via Wilson bases
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- by C. Bargetz, A. Debrouwere and E. A. Nigsch
- Proc. Amer. Math. Soc. 150 (2022), 3841-3852
- DOI: https://doi.org/10.1090/proc/15895
- Published electronically: May 20, 2022
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Abstract:
We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases generated by compactly supported smooth windows. Furthermore, we show that these kind of bases are common unconditional Schauder bases for all separable spaces occurring in these tables. Our work implies that the Valdivia-Vogt structure tables for test functions and distributions may be interpreted as one large commutative diagram.References
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Bibliographic Information
- C. Bargetz
- Affiliation: Department of Mathematics, Universität Innsbruck, Technikerstraße 13, 6020 Innsbruck, Austria
- MR Author ID: 949175
- ORCID: 0000-0001-8525-0532
- Email: christian.bargetz@uibk.ac.at
- A. Debrouwere
- Affiliation: Department of Mathematics and Data Science, Vrije Universiteit Brussel, Belgium, Pleinlaan 2, 1050 Brussels, Belgium
- MR Author ID: 1154620
- Email: andreas.debrouwere@vub.be
- E. A. Nigsch
- Affiliation: Institute of Analysis and Scientific Computing, TU Wien, 1040 Vienna, Austria
- MR Author ID: 938187
- ORCID: 0000-0002-3932-8957
- Email: eduard.nigsch@tuwien.ac.at
- Received by editor(s): July 1, 2021
- Published electronically: May 20, 2022
- Additional Notes: The second author was supported by FWO-Vlaanderen through the postdoctoral grant 12T0519N
- Communicated by: Ariel Barton
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3841-3852
- MSC (2020): Primary 46F05, 46A45; Secondary 81S30
- DOI: https://doi.org/10.1090/proc/15895
- MathSciNet review: 4446234