Reconstruction of functions from their triple correlations

Abstract : Suppose that A is a subset of an abelian group G. To know the 3-deck of A is to know the number of occurrences in A of translates of each possible multiset {0,a,b}. The concept of the 3-deck of a set is naturally extended to L1 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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Philippe Jaming, Mihahilis N. Kolountzakis. Reconstruction of functions from their triple correlations. New York Journal of Math, 2003, 9, pp.149-164. ⟨hal-00005817⟩

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