COSY seminar: ABSTRACT

The goal of this talk is the describe various tools and questions which are considered relevant for the development of Fourier Analysis and its Applications. Starting with a quick historical summary of the last 200 years and a list of highly practical real-world problems which have been solved with the help of Fourier Analysis (e.g. MP3 coding or the detection of graviational waves).

Given the observed discrepancy between the highly sophisticated world of pure mathematics and applications developed in the engineering community or in phyiscis there is a high need for creating mathematical methods addressing those issues which are relevant for the applications. 

The theory of function spaces, based on principles of linear functional analysis, allows to develop such a frame work. Based on a Banach algebra SO(Rd) of test functions (called Feichtinger algebra in the literature) and its dual, the space of mild distributions, one can create a Banach Gelfand triple, with S0 in L2 in SO*.

This setting is not only useful for the treatment of time-variant signals or the characterization of time-invariant linear systems or generalized stochastic processes, it also sheds some new light on classical methods of Fourier Analysis, such as summability methods.

Obviously only a very small selection of topics in this wide range of topics can be covered. Interested participants may find slides of other talks or papers by the author at his web-page. More precisely at https://nuhagphp.univie.ac.at/home/feitalks.php
and  https://nuhagphp.univie.ac.at/home/feipub_db.php