On a characterization of spectra and tilings

Lagarias et al. (Duke Math. J. 103 (2000) 25–37) established a characterization of spectra and tilings that can be used to prove a conjecture of Jorgensen and Pedersen (J. Fourier Anal. Appl. 5 (1999) 285–302) by Keller’s criterion. Different techniques to prove these facts have also been developed by Iosevich and Pedersen and Kolountzakis. In this expository article, the author presents an elementary approach to obtain a more general form of this characterization that relates spectra and tilings.  2003 Elsevier Inc. All rights reserved.