Soit un groupe compact, connexe et non-abélien. Il est bien connu que le groupe dual peut ne pas contenir des sous-ensembles de type Sidon, infinis et centraux, mais on y trouve toujours, pour chaque , des sous-ensembles de type -Sidon qui sont aussi infinis et centraux. On montre, par une méthode essentiellement constructive, que les ensembles infinis centraux de type -Sidon se trouvent aussi dans chaque sous-ensemble infini de . 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 -Sidon sets for 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.
@article{AIF_1995__45_2_547_0,
author = {Hare, Kathryn E.},
title = {Central sidonicity for compact {Lie} groups},
journal = {Annales de l'Institut Fourier},
pages = {547--564},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {45},
number = {2},
year = {1995},
doi = {10.5802/aif.1464},
mrnumber = {96i:43004},
zbl = {0820.43003},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.1464/}
}
TY - JOUR AU - Hare, Kathryn E. TI - Central sidonicity for compact Lie groups JO - Annales de l'Institut Fourier PY - 1995 SP - 547 EP - 564 VL - 45 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1464/ DO - 10.5802/aif.1464 LA - en ID - AIF_1995__45_2_547_0 ER -
%0 Journal Article %A Hare, Kathryn E. %T Central sidonicity for compact Lie groups %J Annales de l'Institut Fourier %D 1995 %P 547-564 %V 45 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1464/ %R 10.5802/aif.1464 %G en %F AIF_1995__45_2_547_0
Hare, Kathryn E. Central sidonicity for compact Lie groups. Annales de l'Institut Fourier, Tome 45 (1995) no. 2, pp. 547-564. doi : 10.5802/aif.1464. http://archive.numdam.org/articles/10.5802/aif.1464/
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