On some properties of the class of stationary sets

Pascal Lefevre

Colloquium Mathematicae (1998)

  • Volume: 76, Issue: 1, page 1-18
  • ISSN: 0010-1354

Abstract

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Some new properties of the stationary sets (defined by G. Pisier in [12]) are studied. Some arithmetical conditions are given, leading to the non-stationarity of the prime numbers. It is shown that any stationary set is a set of continuity. Some examples of "large" stationary sets are given, which are not sets of uniform convergence.

How to cite

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Lefevre, Pascal. "On some properties of the class of stationary sets." Colloquium Mathematicae 76.1 (1998): 1-18. <http://eudml.org/doc/210549>.

@article{Lefevre1998,
abstract = {Some new properties of the stationary sets (defined by G. Pisier in [12]) are studied. Some arithmetical conditions are given, leading to the non-stationarity of the prime numbers. It is shown that any stationary set is a set of continuity. Some examples of "large" stationary sets are given, which are not sets of uniform convergence.},
author = {Lefevre, Pascal},
journal = {Colloquium Mathematicae},
keywords = {Rajchman sets; sets of continuity; stationary sets; UC sets; random Fourier series; Sidon sets; Riesz products},
language = {eng},
number = {1},
pages = {1-18},
title = {On some properties of the class of stationary sets},
url = {http://eudml.org/doc/210549},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Lefevre, Pascal
TI - On some properties of the class of stationary sets
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 1
SP - 1
EP - 18
AB - Some new properties of the stationary sets (defined by G. Pisier in [12]) are studied. Some arithmetical conditions are given, leading to the non-stationarity of the prime numbers. It is shown that any stationary set is a set of continuity. Some examples of "large" stationary sets are given, which are not sets of uniform convergence.
LA - eng
KW - Rajchman sets; sets of continuity; stationary sets; UC sets; random Fourier series; Sidon sets; Riesz products
UR - http://eudml.org/doc/210549
ER -

References

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  1. [1] B R. Blei, Sidon partitions and p-Sidon sets, Pacific J. Math 65 (1976), 307-313. Zbl0335.43008
  2. [2] J. Bourgain, Une remarque sur les ensembles stationnaires, Publ. Math. Orsay, exp. 2 (1981-82). Zbl0527.60010
  3. [3] M. Bożejko and T. Pytlik, Some types of lacunary Fourier series, Colloq. Math. 25 (1972), 117-124. Zbl0249.43013
  4. [4] M. Dechamps-Gondim, Sur les compacts associés aux ensembles lacunaires, les ensembles de Sidon et quelques problèmes ouverts, Publ. Math. Orsay 84-01 (1984). Zbl0537.43018
  5. [5] F J. J. F. Fournier, Two UC-sets whose union is not a UC set, Proc. Amer. Math. Soc. 84 (1982), 69-72. Zbl0511.43003
  6. [6] J. J. F. Fournier and L. Pigno, Analytic and arithmetic properties of thin sets, Pacific J. Math. 105 (1983), 115-141. Zbl0491.43006
  7. [7] K J. P. Kahane, Some Random Series of Functions, Cambridge Stud. Adv. Math. 5, Cambridge Univ. Press, 1985. 
  8. [8] L P. Lefevre, Sur les ensembles de convergence uniforme, Publ. Math. Orsay 94-24 (1994). 
  9. [9] J. M. López and K. A. Ross, Sidon Sets, Lecture Notes in Pure Appl. Math. 13, Marcel Dekker, New York, 1975. 
  10. [10] M. B. Marcus and G. Pisier, Random Fourier Series with Application to Harmonic Analysis, Ann. of Math. Stud. 101, Princeton Univ. Press, 1981. Zbl0474.43004
  11. [11] M I. M. Miheev, Trigonometric series with gaps, Analysis Math. 9 (1983), 43-55. Zbl0544.10062
  12. [12] G. Pisier, Sur l'espace de Banach des séries de Fourier aléatoires presque sûrement continues, Sem. Géométrie des Espaces de Banach, Ecole Polytechnique, 1977-78. 
  13. [13] G. Pisier, De nouvelles caractérisations des ensembles de Sidon, in: Mathematical Analysis and Applications, Adv. in Math. Suppl. Stud. 7B, Academic Press, 1981, 685-726. 
  14. [14] R. Salem and A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954), 245-301. Zbl0056.29001

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