Sidon sets and Riesz products

Bourgain, Jean. "Sidon sets and Riesz products." Annales de l'institut Fourier 35.1 (1985): 137-148. <http://eudml.org/doc/74662>.

@article{Bourgain1985,
abstract = {Let $G$ be a compact abelian group and $\Gamma $ the dual group. It is shown that if $\Delta \subset \Gamma $ is a Sidon set, then the interpolating measures on $\Lambda $ can be obtained as mean of Riesz products. If $\Lambda $ is a Sidon set tending to infinity, $\Lambda $ is of first type. Our approach yields in fact elementary proofs of certain characterizations of Sidonicity obtained in G. Pisier, C.R.A.S., Paris Ser. A, 286 (1978), 1003–1006 – Math. Anal. and Appl., Part B, Advances in Math., Suppl. Sts. vol. 7, 685-726 – preprint, using random Fourier series.},
author = {Bourgain, Jean},
journal = {Annales de l'institut Fourier},
keywords = {Sidon sets; quasi-independent sets; Riesz products},
language = {eng},
number = {1},
pages = {137-148},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sidon sets and Riesz products},
url = {http://eudml.org/doc/74662},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Bourgain, Jean
TI - Sidon sets and Riesz products
JO - Annales de l'institut Fourier
PY - 1985
PB - Association des Annales de l'Institut Fourier
VL - 35
IS - 1
SP - 137
EP - 148
AB - Let $G$ be a compact abelian group and $\Gamma $ the dual group. It is shown that if $\Delta \subset \Gamma $ is a Sidon set, then the interpolating measures on $\Lambda $ can be obtained as mean of Riesz products. If $\Lambda $ is a Sidon set tending to infinity, $\Lambda $ is of first type. Our approach yields in fact elementary proofs of certain characterizations of Sidonicity obtained in G. Pisier, C.R.A.S., Paris Ser. A, 286 (1978), 1003–1006 – Math. Anal. and Appl., Part B, Advances in Math., Suppl. Sts. vol. 7, 685-726 – preprint, using random Fourier series.
LA - eng
KW - Sidon sets; quasi-independent sets; Riesz products
UR - http://eudml.org/doc/74662
ER -