Functional anaysis, Harmonic analysis
A Rudin–de Leeuw type theorem for functions with spectral gaps
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 fH 1 whose Fourier coefficients f ^(k) vanish for all k𝒦.

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DOI: 10.5802/crmath.208
Classification: 30H10, 30J10, 42A32, 46A55
Dyakonov, Konstantin M. 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
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Dyakonov, Konstantin M. 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. http://www.numdam.org/articles/10.5802/crmath.208/

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