# Ulrik Enstad: Time-frequency analysis on the adeles

**Time: **
Wed 2019-09-04 15.30 - 16.30

**Location: **
Room 31, SU

**Lecturer: **
Ulrik Enstad, Oslo

## Abstract

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.