Sidon sets and Riesz products

Jean Bourgain

Annales de l'institut Fourier (1985)

  • Volume: 35, Issue: 1, page 137-148
  • ISSN: 0373-0956

Abstract

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Let G be a compact abelian group and Γ the dual group. It is shown that if Δ Γ is a Sidon set, then the interpolating measures on Λ can be obtained as mean of Riesz products. If Λ is a Sidon set tending to infinity, Λ 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.

How to cite

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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 -

References

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  1. [1] J. BOURGAIN, Propriétés de décomposition pour les ensembles de Sidon, Bull. Soc. Math. France, 111 (1983), 421-428. Zbl0546.43006MR86f:43007
  2. [2] M. DECHAMPS-GONDIM, Ensembles de Sidon topologiques, Ann. Inst. Fourier, Grenoble, 22-3 (1972), 51-79. Zbl0273.43010MR49 #5731
  3. [3] J.M. LOPEZ, K.A. ROSS, Sidon Sets, LN Pure and Appl. Math., No 13, M. Dekker, New York, 1975. Zbl0351.43008MR55 #13173
  4. [4] G. PISIER, Ensembles de Sidon et processus gaussiens, C.R.A.S, Paris, Ser. A, 286 (1978), 1003-1006. Zbl0377.43007
  5. [5] G. PISIER, De nouvelles caractérisations des ensembles de Sidon, Math. Anal. and Appl., Part B, Advances in Math., Suppl. Sts. Vol. 7, 685-726. Zbl0468.43008MR82m:43011
  6. [6] G. PISIER, Conditions d'entropie et caractérisations arithmétiques des ensembles de Sidon, preprint. Zbl0539.43004
  7. [7] POLYA-SZEGO, Inequalities. 
  8. [8] W. RUDIN, Tigonometric series with gaps, J. Math. Mech., 9 (1960), 203-227. Zbl0091.05802MR22 #6972

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