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HARDY'S THEOREM AND THE SHORT-TIME FOURIER TRANSFORM OF SCHWARTZ FUNCTIONS

Published online by Cambridge University Press:  19 March 2001

KARLHEINZ GRÖCHENIG  and
GEORG ZIMMERMANN
KARLHEINZ GRÖCHENIG
Affiliation:
Department of Mathematics U-9, University of Connecticut, Storrs, CT 06269-3009, USA; groch@math.uconn.edu
GEORG ZIMMERMANN
Affiliation:
Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593 Stuttgart, Germany; gzim@uni-hohenheim.de
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Abstract

The Schwartz space of rapidly decaying test functions is characterized by the decay of the short-time Fourier transform or cross-Wigner distribution. Then a version of Hardy's theorem is proved for the short-time Fourier transform and for the Wigner distribution.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 205 - 214
Copyright
The London Mathematical Society 2001

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