A Rudin–de Leeuw type theorem for functions with spectral gaps

Konstantin M. Dyakonov

doi:10.5802/crmath.208

Analyse fonctionnelle, Analyse harmonique

A Rudin–de Leeuw type theorem for functions with spectral gaps

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

Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 797-803.

Résumé

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 $f \in H^{1}$ whose Fourier coefficients $\hat{f} (k)$ vanish for all $k \in 𝒦$ .

Reçu le : 2021-03-22
Révisé le : 2021-04-03
Accepté le : 2021-04-03
Publié le : 2021-09-02

Zbl

DOI : 10.5802/crmath.208

Classification : 30H10, 30J10, 42A32, 46A55

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Konstantin M. Dyakonov},
     title = {A {Rudin{\textendash}de} {Leeuw} type theorem for functions with spectral gaps},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {797--803},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {7},
     year = {2021},
     doi = {10.5802/crmath.208},
     zbl = {07390662},
     language = {en},
}

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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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