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Group Actions and Singular Martingales II, The Recognition Problem |
Canad. J. Math. 56(2004), 431-448
Published:2004-04-01
Printed: Apr 2004
Printed: Apr 2004
- Joseph Rosenblatt
- Michael Taylor
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 - 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.) |