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Journal of Function Spaces and Applications
Volume 2 (2004), Issue 1, Pages 25-53

Spaces of Test Functions via the STFT

1Department of Mathematics U-9, University of Connecticut, Storrs, CT 06269-3009, USA
2Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593 Stuttgart, Germany

Received 1 March 2003

Academic Editor: Hans Feichtinger

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We characterize several classes of test functions, among them Björck's ultra-rapidly decaying test functions and the Gelfand-Shilov spaces of type S, in terms of the decay of their short-time Fourier transform and in terms of their Gabor coefficients.