Time-frequency analysis on the adeles over the rationals
Journal article, Peer reviewed
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Original versionComptes rendus. Mathematique. 2019, 357 (2), 188-199. 10.1016/j.crma.2018.12.004
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.