Gabor Analysis over Quasicrystals meets Operator Algebras

Petter Nyland (NTNU Trondheim)

Thursday 30th January, 2020 16:00-17:00 Maths 311B


Two fundamental families of operators on the Hilbert space of square-integrable functions are time shifts and frequency shifts. These are the central players in time-frequency analysis. The subfield of Gabor analysis is concerned with frames that arise from time-frequency shifts of a fixed window function, so-called Gabor frames. Typically, these time-frequency shifts range over a lattice in the time-frequency plane. Some 10 years ago, F. Luef connected the work of M. Rieffel from the 80’s on non-commutative tori to Gabor frames over lattices. Thus providing a bridge between operator algebras and time-frequency analysis, which has yielded new results in both fields. Recently, results on Gabor frames over more general point-sets than lattices, such as quasicrystals, have appeared. It is then natural to ask whether one can find a similar connection to operator algebras in this more general setting. I will give a selective overview of this theory, and try to indicate what is different when we pass from lattices to quasicrystals.

Add to your calendar

Download event information as iCalendar file (only this event)