Central sidonicity for compact Lie groups

Hare, Kathryn E.

Annales de l'Institut Fourier, Tome 45 (1995) no. 2, pp. 547-564.

Soit $G$ un groupe compact, connexe et non-abélien. Il est bien connu que le groupe dual $\widehat{G}$ 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 $\widehat{G}$. 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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