Reconstruction of functions from their triple correlations
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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.
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 was necessary as we had missed a very significant article by Grunbaum and Moore. Much more has been proved in the real case and in the cyclic case some results complementgin those of Grunbaum and Moore have been proved
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 was necessary as we had missed a very significant article by Grunbaum and Moore. Much more has been proved in the real case and in the cyclic case some results complementgin those of Grunbaum and Moore have been proved