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CENTRAL INTERPOLATION SETS FOR COMPACT GROUPS AND HYPERGROUPS

Published online by Cambridge University Press:  01 September 2009

DAVID GROW  and
KATHRYN E. HARE
DAVID GROW
Affiliation:
Department of Mathematics and Statistics, University of Missouri–Rolla, Rolla, MO 65409, USA e-mail: [email protected]
KATHRYN E. HARE
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada e-mail: [email protected]
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Abstract

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We prove that every infinite subset of the dual of a compact, connected group contains an infinite, central, weighted I0 set. This yields a new proof of the fact that the duals of such groups admit infinite central p-Sidon sets for each p > 1. We also establish the existence of infinite, weighted I0 sets in the duals of many compact, abelian hypergroups.

Keywords

Primary 43A46secondary 43A6243A30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 593 - 603
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Cartwright, D. and McMullen, J., A structural criterion for the existence of infinite Sidon sets, Pac. J. Math. 96 (1981), 301–317.CrossRefGoogle Scholar
2.Connett, W. and Schwartz, A., Subsets of which support hypergroups with polynomial characters, J. Comput. Appl. Math. 65 (1995), 73–84.CrossRefGoogle Scholar
3.Dooley, T., Central lacunary sets for Lie groups, J. Aust. Math. Soc. 45 (1988), 30–45.CrossRefGoogle Scholar
4.Galindo, J. and Hernandez, S., The concept of boundedness and the Bohr compactification of a MAP abelian group, Fund. Math. 159 (1999), 195–218.CrossRefGoogle Scholar
5.Gallagher, P., Zeroes of group characters, Math. Z. 87 (1965), 363–364.CrossRefGoogle Scholar
6.Givens, B. and Kunen, K., Chromatic numbers and Bohr topologies, Topol. Appl. 131 (2003), 189–202.CrossRefGoogle Scholar
7.Graham, C. and Hare, K., ɛ-Kronecker and I 0 sets in abelian groups, IV: Interpolation by non-negative measures, Studia Math. 177 (2006), 9–24.CrossRefGoogle Scholar
8.Graham, C. and Hare, K., I 0 sets for compact, connected groups: Interpolaton with measures that are non-negative or of small support, J. Aust. Math. Soc. 84 (2008), 199–215.CrossRefGoogle Scholar
9.Graham, C., Hare, K. and Korner, T., ɛ-Kronecker and I 0 sets in abelian groups, II: Sparseness of products of ɛ-Kronecker sets, Math. Proc. Camb. Phil. Soc. 140 (2006), 491–508.CrossRefGoogle Scholar
10.Graham, C. and Lau, A., Relative weak compactness of orbits in Banach spaces associated with locally compact groups, Trans. Am. Math. Soc. 359 (2007), 1129–1160.CrossRefGoogle Scholar
11.Grow, D. and Hare, K., The independence of characters on non-abelian groups, Proc. Am. Math. Soc. 132 (2004), 3641–3651.CrossRefGoogle Scholar
12.Hare, K., Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547–564.CrossRefGoogle Scholar
13.Hare, K., Sidonicity in compact, abelian hypergroups, Colloq. Math. 76 (1998), 171–180.CrossRefGoogle Scholar
14.Hare, K. and Ramsey, T., I 0 sets in non-abelian groups, Math. Proc. Camb. Phil. Soc. 135 (2003), 81–98.CrossRefGoogle Scholar
15.Hare, K. and Wilson, D., Weighted p-Sidon sets, J. Aust. Math. Soc. 61 (1996), 73–95.CrossRefGoogle Scholar
16.Jewitt, R., Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), 1–101.CrossRefGoogle Scholar
17.Kunen, K. and Rudin, W., Lacunarity and the Bohr topology, Math. Proc. Camb. Phil. Soc. 126 (1999), 117–137.CrossRefGoogle Scholar
18.Parker, W., Central Sidon and central Λp sets, J. Aust. Math. Soc. 14 (1972), 62–74.CrossRefGoogle Scholar
19.Price, J., Lie groups and compact groups, London Mathematical Society Lecture Notes Series 25 (Cambridge University Press, Cambridge, UK, 1977).CrossRefGoogle Scholar
20.Ragozin, D., Central measures on compact simple Lie groups, J. Func. Anal. 10 (1972), 212–229.CrossRefGoogle Scholar
21.Ramsey, T., Comparisons of Sidon and I 0 sets, Colloq. Math. 70 (1996), 103–132.CrossRefGoogle Scholar
22.Rider, D., Central lacunary sets, Monatsh. Math. 76 (1972), 328–338.CrossRefGoogle Scholar
23.Szego, G., Orthogonal polynomials (American Mathematical Society, New York, 1975).Google Scholar
24.Varadarajan, V., Lie groups, Lie algebras and their representations (Springer, New York, 1984).CrossRefGoogle Scholar
25.Vrem, R., Independent sets and lacunarity for hypergroups, J. Aust. Math. Soc. 50 (1991) 171–188.CrossRefGoogle Scholar