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.
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.
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Ulrik B.R. Enstad 1; Mads S. Jakobsen 2; Franz Luef 2
@article{CRMATH_2019__357_2_188_0, author = {Ulrik B.R. Enstad and Mads S. Jakobsen and Franz Luef}, title = {Time-frequency analysis on the adeles over the rationals}, journal = {Comptes Rendus. Math\'ematique}, pages = {188--199}, publisher = {Elsevier}, volume = {357}, number = {2}, year = {2019}, doi = {10.1016/j.crma.2018.12.004}, language = {en}, }
Ulrik B.R. Enstad; Mads S. Jakobsen; Franz Luef. Time-frequency analysis on the adeles over the rationals. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 188-199. doi : 10.1016/j.crma.2018.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.12.004/
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