Abstract
Interpolation and Sidon subsets of non-discrete abelian groups. Distinction between metrizable and non-metrizable Γ. Perturbations of I 0 and Sidon sets. A survey of I 0 and Sidon sets for compact non-abelian groups. Characterization in terms of FTR sets. Central lacunarity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This should be the set of equivalence classes, but, as usual, we shall assume that a convenient representative is chosen from each class.
References
F. Baur. Lacunarity on nonabelian groups and summing operators. J. Aust. Math. Soc., 71(1):71–79, 2001.
G. Benke. On the hypergroup structure of central Λ(p) sets. Pacific J. Math., 50:19–27, 1974.
D. Cartwright and J. McMullen. A structural criterion for Sidon sets. Pacific J. Math., 96:301–317, 1981.
M. Déchamps(-Gondim). Ensembles de Sidon topologiques. Ann. Inst. Fourier (Grenoble), 22(3):51–79, 1972.
A. Figá-Talamanca and D. G. Rider. A theorem of Littlewood and lacunary series for compact groups. Pacific J. Math., 16:505–514, 1966.
C. C. Graham and K. E. Hare. I 0 sets for compact, connected groups: interpolation with measures that are nonnegative or of small support. J. Austral. Math. Soc., 84(2): 199–225, 2008.
D. Grow and K. E. Hare. The independence of characters on non-abelian groups. Proc. Amer. Math. Soc., 132(12):3641–3651, 2004.
D. Grow and K. E. Hare. Central interpolation sets for compact groups and hypergroups. Glasgow Math. J., 51(3):593–603, 2009.
A. Harcharras. Fourier analysis, Schur multipliers on S p and non-commutative Λ(p)-sets. Studia Math., 137(3):203–260, 1999.
K. E. Hare and (L.) T. Ramsey. I 0 sets in non-abelian groups. Math. Proc. Cambridge Philos. Soc., 135: 81–98, 2003.
K. E. Hare and D. C. Wilson. A structural criterion for the existence of infinite central Λ(p) sets. Trans. Amer. Math. Soc., 337(2):907–925, 1993.
S. Hartman and C. Ryll-Nardzewski. Almost periodic extensions of functions. Colloquium Math., 12:23–39, 1964.
E. Hewitt and K. A. Ross. Abstract Harmonic Analysis, volume II. Springer-Verlag, Berlin, Heidelberg, New York, 1970.
M. F. Hutchinson. Non-tall compact groups admit infinite Sidon sets. J. Aust. Math. Soc., 23(4):467–475, 1977.
M. B. Marcus and G. Pisier. Random Fourier Series with Applications to Harmonic Analysis, volume 101 of Annals of Math. Studies. Princeton University Press, Princeton, N. J., 1981.
W. Parker. Central Sidon and central Λ p sets. J. Aust. Math. Soc, 14:62–74, 1972.
D. Ragozin. Central measures on compact simple Lie groups. J. Func. Anal., 10:212–229, 1972.
(L.) T. Ramsey. A theorem of C. Ryll-Nardzewski and metrizable l.c.a. groups. Proc. Amer. Math. Soc., 78(2):221–224, 1980.
D. G. Rider. Central lacunary sets. Monatsh. Math., 76:328–338, 1972.
D. G. Rider. Randomly continuous functions and Sidon sets. Duke Math. J., 42:759–764, 1975.
V. S. Varadarajan. Lie groups and Lie algebras and their Representations. Number 102 in Graduate Texts in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, 1984. ISBN 0-387-90969-9.
R. Vrem. Independent sets and lacunarity for hypergroups. J. Austral. Math. Soc., 50(2):171–188, 1991.
D. C. Wilson. On the structure of Sidon sets. Monatsh. für Math., 101:67–74, 1986.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Graham, C.C., Hare, K.E. (2013). Interpolation and Sidon Sets for Groups That Are Not Compact and Abelian. In: Interpolation and Sidon Sets for Compact Groups. CMS Books in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5392-5_11
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5392-5_11
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-5391-8
Online ISBN: 978-1-4614-5392-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)