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I0 SETS FOR COMPACT, CONNECTED GROUPS: INTERPOLATION WITH MEASURES THAT ARE NONNEGATIVE OR OF SMALL SUPPORT

Part of: Harmonic analysis in one variable Abstract harmonic analysis

Published online by Cambridge University Press:  01 April 2008

COLIN C. GRAHAM  and
KATHRYN E. HARE
COLIN C. GRAHAM*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada (email: ccgraham@alum.mit.edu) Mailing address: RR#1–D-156, Bowen Island, BC, V0N 1G0, Canada
KATHRYN E. HARE
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada (email: kehare@uwaterloo.ca)
*
✉For correspondence; e-mail: ccgraham@alum.mit.edu
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Abstract

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In the dual object of an infinite compact, connected group, every infinite Sidon set contains an infinite subset on which full interpolation can be performed using very small classes of measures (discrete measures on arbitrarily small sets or nonnegative discrete measures). In particular, the Figà-Talamanca–Rider subset of an infinite product of compact, connected, simple Lie groups has these kinds of interpolation. This substantially improves previous interpolation results.

Keywords

compact nonabelian groupFatou–Zygmund setsFTR setI setSidon set

MSC classification

Secondary: 42A55: Lacunary series of trigonometric and other functions; Riesz products 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A05: Measures on groups and semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 199 - 215
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The research of the authors is partially supported by NSERC.

References

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