Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces
- Author
- Andreas Debrouwere and Lenny Neyt (UGent)
- Organization
- Project
- Abstract
- We study weighted (PLB)-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining weight system. This generalizes Grothendieck’s classical result that the space OM of slowly increasing smooth functions is ultrabornological to the context of ultradifferentiable functions. Furthermore, we determine the multiplier spaces of Gelfand-Shilov spaces and, by using the above result, characterize when such spaces are ultrabornological. In particular, we show that the multiplier space of the space of Fourier ultrahyperfunctions is ultrabornological, whereas the one of the space of Fourier hyperfunctions is not.
- Keywords
- Ultrabornological (PLB)-spaces, Gelfand-Shilov spaces, multiplier spaces, short-time Fourier transform, Gabor frames, THEOREMS, SUPPORT, LIMITS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8736424
- MLA
- Debrouwere, Andreas, and Lenny Neyt. “Weighted (PLB)-Spaces of Ultradifferentiable Functions and Multiplier Spaces.” MONATSHEFTE FUR MATHEMATIK, vol. 198, no. 1, 2022, pp. 31–60, doi:10.1007/s00605-021-01664-z.
- APA
- Debrouwere, A., & Neyt, L. (2022). Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces. MONATSHEFTE FUR MATHEMATIK, 198(1), 31–60. https://doi.org/10.1007/s00605-021-01664-z
- Chicago author-date
- Debrouwere, Andreas, and Lenny Neyt. 2022. “Weighted (PLB)-Spaces of Ultradifferentiable Functions and Multiplier Spaces.” MONATSHEFTE FUR MATHEMATIK 198 (1): 31–60. https://doi.org/10.1007/s00605-021-01664-z.
- Chicago author-date (all authors)
- Debrouwere, Andreas, and Lenny Neyt. 2022. “Weighted (PLB)-Spaces of Ultradifferentiable Functions and Multiplier Spaces.” MONATSHEFTE FUR MATHEMATIK 198 (1): 31–60. doi:10.1007/s00605-021-01664-z.
- Vancouver
- 1.Debrouwere A, Neyt L. Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces. MONATSHEFTE FUR MATHEMATIK. 2022;198(1):31–60.
- IEEE
- [1]A. Debrouwere and L. Neyt, “Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces,” MONATSHEFTE FUR MATHEMATIK, vol. 198, no. 1, pp. 31–60, 2022.
@article{8736424,
abstract = {{We study weighted (PLB)-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining weight system. This generalizes Grothendieck’s classical result that the space OM of slowly increasing smooth functions is ultrabornological to the context of ultradifferentiable functions. Furthermore, we determine the multiplier spaces of Gelfand-Shilov spaces and, by using the above result, characterize when such spaces are ultrabornological. In particular, we show that the multiplier space of the space of Fourier ultrahyperfunctions is ultrabornological, whereas the one of the space of Fourier hyperfunctions is not.}},
author = {{Debrouwere, Andreas and Neyt, Lenny}},
issn = {{0026-9255}},
journal = {{MONATSHEFTE FUR MATHEMATIK}},
keywords = {{Ultrabornological (PLB)-spaces,Gelfand-Shilov spaces,multiplier spaces,short-time Fourier transform,Gabor frames,THEOREMS,SUPPORT,LIMITS}},
language = {{eng}},
number = {{1}},
pages = {{31--60}},
title = {{Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces}},
url = {{http://doi.org/10.1007/s00605-021-01664-z}},
volume = {{198}},
year = {{2022}},
}
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