Comptes Rendus
no. 6
Mathematical analysis/Harmonic analysis
Density of spaces of trigonometric polynomials with frequencies from a subgroup in Lα-spaces
[Les espaces de polynômes trigonométriques avec fréquences dans un sous-groupe sont denses dans les espaces Lα]

Présenté par : the Editorial Board

Juan Miguel Medina1  ; Lutz Peter Klotz2  ; Manfred Riedel2
1 Universidad de Buenos Aires, Facultad de Ingeniería, Departamento de Matemática and Inst. Argentino de Matemática “A. P. Calderón” – CONICET, Saavedra 15, 3er piso (1083), Buenos Aires, Argentina
2 Fakultät für Mathematik und Informatik, Universität Leipzig, 04109 Leipzig, Germany
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 586-593.

Soit G un groupe abélien, localement compact pour une topologie séparée, H un sous-groupe fermé, Γ le groupe dual de G et μ une mesure de Borel positive ou nulle, régulière et finie sur Γ. Nous donnons des conditions nécessaires et suffisantes pour que l'ensemble des polynômes trigonométriques sur Γ avec fréquences dans H soit dense dans Lα(μ), α∈(0,∞).

Let G be an LCA group, H a closed subgroup, Γ the dual group of G and μ be a regular finite non-negative Borel measure on Γ. We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on Γ with frequencies from H in the space Lα(μ),α∈(0,∞).

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2018.04.021
Juan Miguel Medina 1 ; Lutz Peter Klotz 2 ; Manfred Riedel 2

1 Universidad de Buenos Aires, Facultad de Ingeniería, Departamento de Matemática and Inst. Argentino de Matemática “A. P. Calderón” – CONICET, Saavedra 15, 3er piso (1083), Buenos Aires, Argentina
2 Fakultät für Mathematik und Informatik, Universität Leipzig, 04109 Leipzig, Germany 
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     title = {Density of spaces of trigonometric polynomials with frequencies from a subgroup in {\protect\emph{L}\protect\textsuperscript{\protect\emph{\ensuremath{\alpha}}}-spaces}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {586--593},
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Juan Miguel Medina; Lutz Peter Klotz; Manfred Riedel. Density of spaces of trigonometric polynomials with frequencies from a subgroup in Lα-spaces. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 586-593. doi : 10.1016/j.crma.2018.04.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.021/

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