Foundations of Computational Time-Frequency AnalysisHans G. Feichtinger given at FOCM11 Budapest (06.07.11 17:00) id: 2147 length: 45min status: type: LINK-Presentation: https://nuhagphp.univie.ac.at/dateien/talks/2147_FeiFOMC11A.pdf ABSTRACT: The talk is going to describe the setting of Banach Gelfand Triples as the appropriate frame-work for the description of these approximation processes, indicates existing results and methods used in this field already now, and describes the demand for further research in order to improve from qualitative asymptotic to quantitative results, in the spirit of approximation theory. So whatever should be computed (e.g. a dual Gabor atom, the action of a pseudo-differential operator on an $L^2$-function, etc.) one should have tools to describe, how a realizable (by actual computation, using finitely many matrices etc.) approximation can be achieved by suitable, hopefully at least suboptimal, procedures, which allow to compute the entity under consideration up to a given $\varepsilon 0$ or up to a given relative error in some appropriate norm (such as a Sobolev norm or a Shubin norm). It will be demonstrated that the interplay between functional analysis, harmonic and numerical analysis and approximation theory can be provide such methods. |