Random weighted Sidon sets

Kathryn Hare

Colloquium Mathematicae (2000)

  • Volume: 86, Issue: 1, page 103-109
  • ISSN: 0010-1354

Abstract

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We investigate random Sidon-type sets in which the degrees of the representations are weighted. These variants of Sidon sets are of interest as there are compact non-abelian groups which admit no infinite Sidon sets. In this note we determine the largest weight function such that infinite random weighted Sidon sets exist in all infinite compact groups.

How to cite

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Hare, Kathryn. "Random weighted Sidon sets." Colloquium Mathematicae 86.1 (2000): 103-109. <http://eudml.org/doc/210833>.

@article{Hare2000,
abstract = {We investigate random Sidon-type sets in which the degrees of the representations are weighted. These variants of Sidon sets are of interest as there are compact non-abelian groups which admit no infinite Sidon sets. In this note we determine the largest weight function such that infinite random weighted Sidon sets exist in all infinite compact groups.},
author = {Hare, Kathryn},
journal = {Colloquium Mathematicae},
keywords = {compact non-abelian groups; Sidon sets; compact non-abelian group; Lie group; local weighted Sidon set; random local weighted Sidon set; random weighted Sidon set; weighted Sidon set},
language = {eng},
number = {1},
pages = {103-109},
title = {Random weighted Sidon sets},
url = {http://eudml.org/doc/210833},
volume = {86},
year = {2000},
}

TY - JOUR
AU - Hare, Kathryn
TI - Random weighted Sidon sets
JO - Colloquium Mathematicae
PY - 2000
VL - 86
IS - 1
SP - 103
EP - 109
AB - We investigate random Sidon-type sets in which the degrees of the representations are weighted. These variants of Sidon sets are of interest as there are compact non-abelian groups which admit no infinite Sidon sets. In this note we determine the largest weight function such that infinite random weighted Sidon sets exist in all infinite compact groups.
LA - eng
KW - compact non-abelian groups; Sidon sets; compact non-abelian group; Lie group; local weighted Sidon set; random local weighted Sidon set; random weighted Sidon set; weighted Sidon set
UR - http://eudml.org/doc/210833
ER -

References

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  1. [1] K. Adams, Weighted Sidon sets, Ph.D. dissertation, Univ. of Missouri, 1998. 
  2. [2] K. Adams and D. Grow, Lacunary series on compact groups, this issue, 1-7. 
  3. [3] A. Dooley, Central lacunary sets for Lie groups, J. Austral. Math. Soc. 45 (1988), 30-45. Zbl0689.43003
  4. [4] A. Dooley and P. Soardi, Local p-Sidon sets for Lie groups, Proc. Amer. Math. Soc. 72 (1978), 125-126. Zbl0398.43008
  5. [5] K. Hare, The size of characters of compact Lie groups, Studia Math. 129 (1998), 1-18. Zbl0946.43006
  6. [6] K. Hare and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95. Zbl0874.43005
  7. [7] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Springer, New York, 1979. Zbl0416.43001
  8. [8] J. López and K. Ross, Sidon Sets, Marcel Dekker, New York, 1975. 
  9. [9] M. Marcus and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Ann. of Math. Stud. 101, Princeton Univ. Press, Princeton, 1981. Zbl0474.43004
  10. [10] W. Parker, Central Sidon and central Λ ( p ) sets, J. Austral. Math. Soc. 14 (1972), 62-74. Zbl0237.43004
  11. [11] D. Ragozin, Central measures on compact simple Lie groups, J. Funct. Anal. 10 (1972), 212-229. Zbl0286.43002
  12. [12] D. Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764. Zbl0345.43008
  13. [13] S. Sidon, Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken, Math. Ann. 97 (1927), 675-676. Zbl53.0252.02

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