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Approximation of continuous problems in Fourier Analysis by finite dimensional ones: The setting of the Banach Gelfand Triple

Presented by: 
Hans Feichtinger University of Vienna, University of Vienna
Date: 
Wednesday 19th June 2019 - 11:10 to 12:00
Venue: 
INI Seminar Room 1
Abstract: 
When it comes to the constructive realization of operators arising in Fourier Analysis, be it the Fourier transform itself, or some convolution operator, or more generally an (underspread) pseudo-diferential operator it is natural to make use of sampled version of the ingredients. The theory around the Banach Gelfand Triple (S0,L2,SO') which is based on methods from Gabor and time-frequency analysis, combined with the
relevant function spaces (Wiener amalgams and modulation spaces) allows to provide what we consider the appropriate setting and possibly the starting point for qualitative as well as later on more quantitative
error estimates.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons