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Group Actions and Singular Martingales II, The Recognition Problem

Published online by Cambridge University Press:  20 November 2018

Joseph Rosenblatt  and
Michael Taylor
Joseph Rosenblatt
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA e-mail: jrsnbltt@math.uiuc.edu
Michael Taylor
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA e-mail: met@math.unc.edu
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Abstract

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We continue our investigation in [RST] of a martingale formed by picking a measurable set $A$ in a compact group $G$, taking random rotates of $A$, and considering measures of the resulting intersections, suitably normalized. Here we concentrate on the inverse problem of recognizing $A$ from a small amount of data from this martingale. This leads to problems in harmonic analysis on $G$, including an analysis of integrals of products of Gegenbauer polynomials.

Keywords

43A7760B1560G4242C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 2 , 01 April 2004 , pp. 431 - 448
Copyright
Copyright © Canadian Mathematical Society 2004

References

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