Reconstruction of functions from their triple correlations

Philippe Jaming (1) , Mihahilis N. Kolountzakis (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics

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.

Mots clés: k-deck; phase retrieval; bispectrum; triple correlation

Domaines: Analyse classique [math.CA]

Philippe Jaming, Mihahilis N. Kolountzakis. Reconstruction of functions from their triple correlations. New York Journal of Math, 2003, 9, pp.149-164. ⟨hal-00005817⟩