NuHAG :: TALKS

Talks given at NuHAG events

Foundations of Computational Time-Frequency Analysis


  Hans 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.


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