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The Pompeiu problem for groups

Published online by Cambridge University Press:  24 October 2008

Alan L. Carey ,
Eberhard Kaniuth  and
William Moran
Alan L. Carey
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide Sit 5001, Australia
Eberhard Kaniuth
Affiliation:
Fachbereich Mathematik/informatik, Universität Paderborn, D-4790 Paderborn, Federal Republic of Germany
William Moran
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide SA 5001, Australia
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Extract

The Pompeiu problem has its origins in classical analysis in ℝn (see [2, 3, 4, 8] for a discussion and some history). In this context it may be stated as follows. Let D ⊂ ℝn be a bounded measurable set of positive Lebesgue measure and f a locally integrable function on ℝn. Then, if ∫σ(D)f = 0 for all rigid motions σ of ℝn, is f = 0?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 45 - 58
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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