A Rudin–de Leeuw type theorem for functions with spectral gaps
Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space $H^1$. We extend this result to subspaces of $H^1$ formed by functions with smaller spectra. More precisely, given a finite set $\mathcal{K}$ of positive integers, we prove a R...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.208/ |
| Summary: | Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space $H^1$. We extend this result to subspaces of $H^1$ formed by functions with smaller spectra. More precisely, given a finite set $\mathcal{K}$ of positive integers, we prove a Rudin–de Leeuw type theorem for the unit ball of $H^1_{\mathcal{K}}$, the space of functions $f\in H^1$ whose Fourier coefficients $\widehat{f}(k)$ vanish for all $k\in \mathcal{K}$. |
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| ISSN: | 1778-3569 |