Hare, Kathryn E.
Central sidonicity for compact Lie groups
Annales de l'institut Fourier, Tome 45 (1995) no. 2 , p. 547-564
Zbl 0820.43003 | MR 96i:43004
doi : 10.5802/aif.1464
URL stable : http://www.numdam.org/item?id=AIF_1995__45_2_547_0

Soit G un groupe compact, connexe et non-abélien. Il est bien connu que le groupe dual G ^ peut ne pas contenir des sous-ensembles de type Sidon, infinis et centraux, mais on y trouve toujours, pour chaque p>1, des sous-ensembles de type p-Sidon qui sont aussi infinis et centraux. On montre, par une méthode essentiellement constructive, que les ensembles infinis centraux de type p-Sidon se trouvent aussi dans chaque sous-ensemble infini de G ^. Aussi étudions-nous, pour un groupe de Lie compact, la connexion entre sa sidonicité centrale et la sidonicité de son tore.
It is known that the dual of a compact, connected, non-abelian group may contain no infinite central Sidon sets, but always does contain infinite central p-Sidon sets for p>1. We prove, by an essentially constructive method, that the latter assertion is also true for every infinite subset of the dual. In addition, we investigate the relationship between weighted central Sidonicity for a compact Lie group and Sidonicity for its torus.

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