Comptes Rendus
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Functional anaysis, Harmonic analysis
A Rudin–de Leeuw type theorem for functions with spectral gaps
Konstantin M. Dyakonov1, 2  
1 Departament de Matemàtiques i Informàtica, IMUB, BGSMath, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain
2 ICREA, Pg. Lluís Companys 23, E-08010 Barcelona, Spain
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 797-803.

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 𝒦 of positive integers, we prove a Rudin–de Leeuw type theorem for the unit ball of H 𝒦 1 , the space of functions f∈H 1 whose Fourier coefficients f ^(k) vanish for all k∈𝒦.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.208
Classification: 30H10, 30J10, 42A32, 46A55

Konstantin M. Dyakonov 1, 2

1 Departament de Matemàtiques i Informàtica, IMUB, BGSMath, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain
2 ICREA, Pg. Lluís Companys 23, E-08010 Barcelona, Spain
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Konstantin M. Dyakonov. A Rudin–de Leeuw type theorem for functions with spectral gaps. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 797-803. doi : 10.5802/crmath.208. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.208/

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