 

Philippe Jaming and Mihail N. Kolountzakis
Reconstruction of functions from their triple correlations


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


Abstract
Suppose that A is a subset of an abelian group G.
To know the 3deck of A is to know the number of
occurrences in A of translates of each possible
multiset {0,a,b}.
The concept of the 3deck of a set is naturally extended to
L^{1} functions on G.
In this paper we study when the 3deck 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.


Acknowledgements
Research partially financed by: European Commission Harmonic Analysis and Related Problems 20022006 IHP Network (Contract Number: HPRNCT200100273  HARP)


Author information
Philippe Jaming:
Université d'Orléans, Faculté des Sciences, Département de Mathématiques, BP 6759, F 45067 Orléans Cedex 2, France
jaming@labomath.univorleans.fr
http://www.univorleans.fr/SCIENCES/MAPMO/membres/jaming/
Mihail N. Kolountzakis:
Department of Mathematics, University of Crete, Knossos Ave., 714 09 Iraklio, Greece
kolount@member.ams.org
http://fourier.math.uoc.gr/~mk/

