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Group Actions and Singular Martingales II, The Recognition Problem

  Published:2004-04-01
 Printed: Apr 2004
  • Joseph Rosenblatt
  • Michael Taylor
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Abstract

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.
MSC Classifications: 43A77, 60B15, 60G42, 42C10 show english descriptions Analysis on general compact groups
Probability measures on groups or semigroups, Fourier transforms, factorization
Martingales with discrete parameter
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
43A77 - Analysis on general compact groups
60B15 - Probability measures on groups or semigroups, Fourier transforms, factorization
60G42 - Martingales with discrete parameter
42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
 

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