# Random weighted Sidon sets

Colloquium Mathematicae (2000)

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

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topHare, 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

top- [1] K. Adams, Weighted Sidon sets, Ph.D. dissertation, Univ. of Missouri, 1998.
- [2] K. Adams and D. Grow, Lacunary series on compact groups, this issue, 1-7.
- [3] A. Dooley, Central lacunary sets for Lie groups, J. Austral. Math. Soc. 45 (1988), 30-45. Zbl0689.43003
- [4] A. Dooley and P. Soardi, Local p-Sidon sets for Lie groups, Proc. Amer. Math. Soc. 72 (1978), 125-126. Zbl0398.43008
- [5] K. Hare, The size of characters of compact Lie groups, Studia Math. 129 (1998), 1-18. Zbl0946.43006
- [6] K. Hare and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95. Zbl0874.43005
- [7] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Springer, New York, 1979. Zbl0416.43001
- [8] J. López and K. Ross, Sidon Sets, Marcel Dekker, New York, 1975.
- [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] W. Parker, Central Sidon and central $\Lambda \left(p\right)$ sets, J. Austral. Math. Soc. 14 (1972), 62-74. Zbl0237.43004
- [11] D. Ragozin, Central measures on compact simple Lie groups, J. Funct. Anal. 10 (1972), 212-229. Zbl0286.43002
- [12] D. Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764. Zbl0345.43008
- [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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