New York Journal of Mathematics
Volume 9 (2003) 149-164


Philippe Jaming and Mihail N. Kolountzakis

Reconstruction of functions from their triple correlations

Published: October 23, 2003
Keywords: k-deck; phase retrieval; bispectrum; triple correlation
Subject: 42A99; 94A12

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.


Research partially financed by: European Commission Harmonic Analysis and Related Problems 2002-2006 IHP Network (Contract Number: HPRN-CT-2001-00273 - HARP)

Author information

Philippe Jaming:
Université d'Orléans, Faculté des Sciences, Département de Mathématiques, BP 6759, F 45067 Orléans Cedex 2, France

Mihail N. Kolountzakis:
Department of Mathematics, University of Crete, Knossos Ave., 714 09 Iraklio, Greece