A qualitative uncertainty principle for unimodular groups of type

Author:
Jeffrey A. Hogan

Journal:
Trans. Amer. Math. Soc. **340** (1993), 587-594

MSC:
Primary 43A30; Secondary 43A25

MathSciNet review:
1102222

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Abstract: It has long been known that if and the supports of and its Fourier transform are bounded then almost everywhere. More recently it has been shown that the same conclusion can be reached under the weaker condition that the supports of and have finite measure. These results may be thought of as qualitative uncertainty principles since they limit the "concentration" of the Fourier transform pair . Little is known, however, of analogous results for functions on locally compact groups. A qualitative uncertainty principle is proved here for unimodular groups of type I.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1993-1102222-4

Keywords:
Fourier transform,
unimodular groups of type I

Article copyright:
© Copyright 1993
American Mathematical Society