Reconstruction of functions from their triple correlations

Details Reconstruction of functions from their triple correlations Reconstruction of functions from their triple correlations

2002-07-04

arxiv.org/abs/math/0207051v2

Mathematics

Classical Analysis and ODEs

17 pages, preprint. This is a generous revision of our paper with the same title that was posted on the Arxiv a year ago. This

Scientific paper

Suppose that A is a subset of an abelian group G. To know the 3-deck of A is to know the number of occurences in A of translates of each possible multiset {0,a,b}. The concept of the 3-deck is naturally extended to integrable functions on G. In this paper we study when the 3-deck of a function determines the function up to translations. The method is to look at the Fourier Transform of the function. Our emphasis is on the real line and the cyclic groups.

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