15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 7 - Funktionalanalysis, Harmonische Analysis
Montag, 17. September 2001, 17.00, Hörsaal 28

 

Spaces of Test Functions via the Short Time Fourier Transform

Georg Zimmermann, Universität Hohenheim (Koautor: Karlheinz Gröchenig)

 

We show how the Björck spaces of ultra-rapidly decaying test functions and the Gelfand-Shilov spaces of type $\mathbf S$ can be described via the Short Time Fourier Transform. We also point out connections with the so-called modulation spaces (e.g., see [1]). These spaces are characterized by the global behaviour of the short-time Fourier transform of its members. They are the appropriate frame-work to describe function spaces by means of Gabor frames, in a way similar to the characterization of Besov spaces via wavelet expansions.

[1]	H.G. Feichtinger, K. Gröchenig, and D. Walnut, Wilson Bases and Modulation Spaces, Math. Nachr. 155 (1992), pp. 7-17.

E-Mail:	gzim@uni-hohenheim.de
Homepage:	www.uni-hohenheim.de/~gzim

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