Central sidonicity for compact Lie groups

Kathryn E. Hare

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 2, page 547-564
  • ISSN: 0373-0956

Abstract

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It is known that the dual of a compact, connected, non-abelian group may contain no infinite central Sidon sets, but always does contain infinite central p -Sidon sets for p > 1 . We prove, by an essentially constructive method, that the latter assertion is also true for every infinite subset of the dual. In addition, we investigate the relationship between weighted central Sidonicity for a compact Lie group and Sidonicity for its torus.

How to cite

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Hare, Kathryn E.. "Central sidonicity for compact Lie groups." Annales de l'institut Fourier 45.2 (1995): 547-564. <http://eudml.org/doc/75128>.

@article{Hare1995,
abstract = {It is known that the dual of a compact, connected, non-abelian group may contain no infinite central Sidon sets, but always does contain infinite central $p$-Sidon sets for $p&gt;1.$ We prove, by an essentially constructive method, that the latter assertion is also true for every infinite subset of the dual. In addition, we investigate the relationship between weighted central Sidonicity for a compact Lie group and Sidonicity for its torus.},
author = {Hare, Kathryn E.},
journal = {Annales de l'institut Fourier},
keywords = {compact connected non-Abelian groups; central Sidon sets; central - Sidon sets; dual groups; weighted central Sidonicity; compact Lie groups},
language = {eng},
number = {2},
pages = {547-564},
publisher = {Association des Annales de l'Institut Fourier},
title = {Central sidonicity for compact Lie groups},
url = {http://eudml.org/doc/75128},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Hare, Kathryn E.
TI - Central sidonicity for compact Lie groups
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 2
SP - 547
EP - 564
AB - It is known that the dual of a compact, connected, non-abelian group may contain no infinite central Sidon sets, but always does contain infinite central $p$-Sidon sets for $p&gt;1.$ We prove, by an essentially constructive method, that the latter assertion is also true for every infinite subset of the dual. In addition, we investigate the relationship between weighted central Sidonicity for a compact Lie group and Sidonicity for its torus.
LA - eng
KW - compact connected non-Abelian groups; central Sidon sets; central - Sidon sets; dual groups; weighted central Sidonicity; compact Lie groups
UR - http://eudml.org/doc/75128
ER -

References

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  1. [1] D.I. CARTWRIGHT and J.R. MCMULLEN, A structural criterion for the existence of infinite Sidon sets, Pacific J. Math., 96 (1981), 301-317. Zbl0445.43006MR83c:43009
  2. [2] R. COIFMAN and G. WEISS, Central multiplier theorems for compact Lie groups, Bull. Amer. Math. Soc., 80 (1974), 124-126. Zbl0276.43009MR48 #9271
  3. [3] A.H. DOOLEY, Central lacunary sets for Lie groups, J. Aust. Math. Soc., 45 (1988), 30-45. Zbl0689.43003MR89j:43007
  4. [4] P. GALLAGHER, Zeroes of group characters, Math. Z., 87 (1965), 363-364. Zbl0128.25602MR31 #276
  5. [5] K. HARE and D. WILSON, Weighted p-Sidon sets, J. Aust. Math. Soc., to appear. Zbl0874.43005
  6. [6] E. HEWITT and K. ROSS, Abstract harmonic analysis II, Springer-Verlag, New York, 1970. Zbl0213.40103
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  8. [8] J. LOPEZ and K. ROSS, Sidon sets, Lecture Notes Pure Appl. Math., No. 13, Marcel Dekker, New York, 1975. Zbl0351.43008MR55 #13173
  9. [9] W.A. PARKER, Central Sidon and central Λ(p) sets, J. Aust. Math. Soc., 14 (1972), 62-74. Zbl0237.43004MR47 #9178
  10. [10] J.F. PRICE, Lie groups and compact groups, London Math. Soc. Lecture Note Series No.25, Cambridge Univ. Press, Cambridge, 1977. Zbl0348.22001MR56 #8743
  11. [11] D.L. RAGOZIN, Central measures on compact simple Lie groups, J. Func. Anal., 10 (1972), 212-229. Zbl0286.43002MR49 #5715
  12. [12] D. RIDER, Central lacunary sets, Monatsh. Math., 76 (1972), 328-338. Zbl0258.43008MR51 #3801
  13. [13] R. STANTON and P. TOMAS, Polyhedral summability of Fourier series on compact Lie groups, Amer. J. Math., 100 (1978), 477-493. Zbl0421.43009MR58 #29855
  14. [14] V.S. VARADARAJAN, Lie groups, Lie algebras and their representations, Springer-Verlag, New York, 1984. Zbl0955.22500

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