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Ulrik Enstad: Time-frequency analysis on the adeles

Time: Wed 2019-09-04 15.30 - 16.30

Location: Room 31, SU

Participating: Ulrik Enstad, Oslo

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A central problem in time-frequency analysis is to determine when a set
of time-frequency shifts of a given function forms a frame for the
Hilbert space \(L^2(\mathbb{R}^n)\). Such frames are called Gabor frames,
and they are related to the representation theory of the Heisenberg
group. Time-frequency analysis can be done in the setting of a locally
compact abelian group, but \(\mathbb{R}^n\)has received the most
attention so far. In this talk, we show that a class of number theoretic
groups, including the rational adeles group, provides interesting
examples. In particular, we construct Gabor frames in this setting, and
show that a Balian-Low theorem holds. This is joint work with Mads
Sielemann Jakobsen, Franz Luef and Tron Omland.