Central sidonicity for compact Lie groups
Annales de l'Institut Fourier, Volume 45 (1995) no. 2, p. 547-564

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.

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.

@article{AIF_1995__45_2_547_0,
     author = {Hare, Kathryn E.},
     title = {Central sidonicity for compact Lie groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {2},
     year = {1995},
     pages = {547-564},
     doi = {10.5802/aif.1464},
     zbl = {0820.43003},
     mrnumber = {96i:43004},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1995__45_2_547_0}
}
Central sidonicity for compact Lie groups. Annales de l'Institut Fourier, Volume 45 (1995) no. 2, pp. 547-564. doi : 10.5802/aif.1464. http://www.numdam.org/item/AIF_1995__45_2_547_0/

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