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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 {\em $3$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 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.

Acknowledgments:
Research partially financed by: {\it European Commission} Harmonic Analysis and Related Problems 20022006 IHP Network (Contract Number: HPRNCT200100273  HARP)
Author information:
Philippe Jaming :
Universit\'e d'Orl\'eans, Facult\'e des Sciences, D\'epartement de Ma\th\'e\ma\ti\ques, BP 6759, F 45067 Orl\'eans 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/
 