Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T08:27:15.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-tall compact groups admit infinite Sidon sets

Published online by Cambridge University Press:  09 April 2009

M. F. Hutchinson
M. F. Hutchinson
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, N.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Riesz polynomials are employed to give a sufficient condition for a non-abelian compact group G to have an infinite uniformly approximable Sidon set. This condition is satisfied if G admits infinitely many pairwise inequivalent continuous irreducible unitary representations of the same degree. Consequently a compact Lie group admits an infinite Sidon set if and only if it is not semi-simple.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 467 - 475
Copyright
Copyright © Australian Mathematical Society 1977

References

Cecchini, Carlo (1972), ‘Lacunary Fourier series on compact Lie groups’, J. Functional Analysis 11, 191–203.CrossRefGoogle Scholar
Dunkl, C. F. and Ramirez, D. E. (1971a), ‘Sidon sets on compact groups’, Monatsh. Math. 75, 111–117.CrossRefGoogle Scholar
Dunkl, C. F. and Ramirez, D. E. (1971b), ‘Central Sidon sets of bounded representation type’, Notices Amer. Math. Soc. 18, 1101.Google Scholar
Alessandro, Figà-Talamanca (1967), ‘Appartenenza a Lp delle serie di Fourier aleatorie su gruppi non commutativi’, Rend. Sem. Mat. Univ. Padova 39, 330–348.Google Scholar
Gantmacher, F. R. (1958), Matrizenrechnung, Teil I (Veb Deutscher Verlag der Wissenschaften, Berlin, 1958).Google Scholar
Helgason, S. (1962), Differential Geometry and Symmetric Spaces (Academic Press, New York, 1962).Google Scholar
Hewitt, E. and Ross, K. R. (1970), Abstract Harmonic Analysis, Vol. II (Springer-Verlag, Berlin, 1970).Google Scholar
McMullen, J. R. and Price, J. F. (1976), ‘Rudin Shapiro sequences for arbitrary compact groups’, J. Austral. Math. Soc. 22 (Series A), 421–430.CrossRefGoogle Scholar
Parker, Willard A. (1972), ‘Central Sidon and Central Λp sets’, J. Austral. Math. Soc. 14, 62–72.CrossRefGoogle Scholar
Pontryagin, L. S. (1939), Topological Groups (Princeton University Press, Princeton, 1939).Google Scholar
Rider, Daniel (1966), ‘Gap series on circles and spheres’, Canad. J. Math. 18, 389–398.CrossRefGoogle Scholar
Rider, Daniel (1972), ‘Central lacunary sets’, Monatsch Math. 76, 328–338.CrossRefGoogle Scholar