Title: Time-frequency analysis and suitable function spaces
Speaker: Hans Georg Feichtinger (Institute of Mathematics, University of Vienna, Austria)
Date: 06 January 2021
Time: 4 pm
Venue: Zoom (online)
The key-point of this talk will be some exploration of
function spaces concepts arising from time-frequency analysis
respectively Gabor Analysis. Modulation spaces and Wiener
amalgams have proved to be indispensable tools in time-frequency
analysis, but also for the treatment of pseudo-differential
operators or Fourier integral operators.
More precisely, we will recall a short summary of the concepts
of Wiener amalgam spaces and modulation spaces, as well as the
concept of Banach Gelfand Triples, with the associated kernel
theorem (in the spirit of the L. Schwartz kernel theorem).
We will indicate in which sense these spaces allow to
capture more precisely the mapping properties of operators
which may be unbounded in the Hilbert space setting.
The subfamily of translation and modulation invariant spaces
plays a specific role, with naturally associated regularization
operators involving smoothing by convolution and localization
by pointwise multiplication.