# Ulrik Enstad: Bases generated by unitary representations via group operator algebras

**Time: **
Wed 2021-10-06 13.15 - 14.15

**Location: **
Zoom, meeting ID: 694 6016 6420 (password required)

**Lecturer: **
Ulrik Enstad (SU)

**Abstract:**

In harmonic analysis and signal processing, bases and frames provide a means to decompose complicated functions into simpler building blocks. Many such bases, examples being Gabor frames and wavelets, share the property that they lie in the orbit of an irreducible representation of a Lie group. When sampling from a lattice, the existence (or lack thereof) of such bases and frames can be naturally approached using von Neumann algebras, as shown by B. Bekka. In this talk I want to discuss the analogous problem for well-localized bases, e.g. bases generated by smooth vectors. In particular, I will show that recent machinery from the classification program for nuclear C*-algebras can be used to prove new existence results for bases generated by representations of nilpotent Lie groups. This is joint work with E. Bédos and J. T. van Velthoven.

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