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/ |
| _version_ | 1797651544099782656 |
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| author | Dyakonov, Konstantin M. |
| author_facet | Dyakonov, Konstantin M. |
| author_sort | Dyakonov, Konstantin M. |
| collection | DOAJ |
| description | 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 $k\in \mathcal{K}$. |
| first_indexed | 2024-03-11T16:16:20Z |
| format | Article |
| id | doaj.art-75db9aee87834be584cf42642f9e6089 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:20Z |
| publishDate | 2021-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-75db9aee87834be584cf42642f9e60892023-10-24T14:19:25ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-09-01359779780310.5802/crmath.20810.5802/crmath.208A Rudin–de Leeuw type theorem for functions with spectral gapsDyakonov, Konstantin M.0https://orcid.org/0000-0002-9232-6264Departament de Matemàtiques i Informàtica, IMUB, BGSMath, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain; ICREA, Pg. Lluís Companys 23, E-08010 Barcelona, SpainOur 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 $k\in \mathcal{K}$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.208/ |
| spellingShingle | Dyakonov, Konstantin M. A Rudin–de Leeuw type theorem for functions with spectral gaps Comptes Rendus. Mathématique |
| title | A Rudin–de Leeuw type theorem for functions with spectral gaps |
| title_full | A Rudin–de Leeuw type theorem for functions with spectral gaps |
| title_fullStr | A Rudin–de Leeuw type theorem for functions with spectral gaps |
| title_full_unstemmed | A Rudin–de Leeuw type theorem for functions with spectral gaps |
| title_short | A Rudin–de Leeuw type theorem for functions with spectral gaps |
| title_sort | rudin de leeuw type theorem for functions with spectral gaps |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.208/ |
| work_keys_str_mv | AT dyakonovkonstantinm arudindeleeuwtypetheoremforfunctionswithspectralgaps AT dyakonovkonstantinm rudindeleeuwtypetheoremforfunctionswithspectralgaps |