Group Actions and Singular Martingales II, The Recognition Problem

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

[学科分类] 数学（综合）