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

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ASCW03 - Approximation, sampling, and compression in high dimensional problems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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