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A note on Riesz sets and lacunary sets

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

R. G. M. Brummelhuis
R. G. M. Brummelhuis
Affiliation:
Department of Mathematics, University of AmsterdamPlantage Muidergracht 24 1018 TV Amsterdam The Netherlands
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Abstract

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W. Rudin has proved that the union of the Riesz set N ⊆ R with a Λ(l)-subset of Z is again a Riesz set. In this note we generalize his result to compact groups whose contains a circle group, thereby extending an earlier F. and M. Riesz theorem for such groups by the author. We also investigate the possibility of constructing Λ(p)-sets for these groups, departing from Λ(p)-sets for the circle group in center.

MSC classification

Secondary: 43A05: Measures on groups and semigroups, etc. 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 22E30: Analysis on real and complex Lie groups 43A77: Analysis on general compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 57 - 65
Copyright
Copyright © Australian Mathematical Society 1990

References

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