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Comptes Rendus Mathématique
Volume 357, n° 2
pages 188-199 (février 2019)
Doi : 10.1016/j.crma.2018.12.004
Received : 27 July 2018 ;  accepted : 7 January 2019
Time-frequency analysis on the adeles over the rationals
Analyse des temps-fréquences sur l'anneau des adèles des rationnels

Ulrik B.R. Enstad a , Mads S. Jakobsen b , Franz Luef b
a University of Oslo, Department of Mathematics, Oslo, Norway 
b Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway 


We show that the construction of Gabor frames in   with generators in   and with respect to time-frequency shifts from a rectangular lattice   is equivalent to the construction of certain Gabor frames for   over the adeles over the rationals and the group  . Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on   with the construction of certain Heisenberg modules.

The full text of this article is available in PDF format.

Nous montrons que la construction de trames (ou repères) de Gabor de   avec générateurs dans   et des décalages de temps-fréquence dans un réseau rectangulaire   est équivalente à la construction de certaines trames de Gabor pour   sur les adèles des rationnels avec le groupe  . Nous analysons également les relations entre la construction de trames de Gabor sur les adèles et sur   et la construction de certains modules de Heisenberg.

The full text of this article is available in PDF format.

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