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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A qualitative uncertainty principle for unimodular groups of type $ {\rm I}$


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 $ f \in {L^2}({{\mathbf{R}}^n})$ and the supports of and its Fourier transform $ \hat f$ are bounded then $ f = 0$ almost everywhere. More recently it has been shown that the same conclusion can be reached under the weaker condition that the supports of $ f$ and $ \hat f$ have finite measure. These results may be thought of as qualitative uncertainty principles since they limit the "concentration" of the Fourier transform pair $ (f,\hat f)$. 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
PII: S 0002-9947(1993)1102222-4
Keywords: Fourier transform, unimodular groups of type I
Article copyright: © Copyright 1993 American Mathematical Society