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Non-extendability of the finite Hilbert transform
Citation
Curbera, GP and Okada, S and Ricker, WJ, Non-extendability of the finite Hilbert transform, Monatshefte fur Mathematik, 195, (4) pp. 649-657. ISSN 0026-9255 (2021) [Refereed Article]
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Copyright Statement
Copyright (2021) TheAuthor(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.
DOI: doi:10.1007/s00605-021-01572-2
Abstract
The finite Hilbert transform T:X -> X acts continuously on every rearrangement invariant space X on (-1,1) having non-trivial Boyd indices. It is proved that T cannot be further extended, whilst still taking its values in X, to any larger domain space. That is, T:X -> X is already optimally defined.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Research Division: | Mathematical Sciences |
| Research Group: | Pure mathematics |
| Research Field: | Pure mathematics not elsewhere classified |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding knowledge |
| Objective Field: | Expanding knowledge in the mathematical sciences |
| UTAS Author: | Okada, S (Dr Susumu Okada) |
| ID Code: | 152494 |
| Year Published: | 2021 |
| Deposited By: | Mathematics |
| Deposited On: | 2022-08-19 |
| Last Modified: | 2022-09-14 |
| Downloads: | 3 View Download Statistics |
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