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A Qualitative Uncertainty Principle for Unimodular Groups of Type I

Jeffrey A. Hogan
Transactions of the American Mathematical Society
Vol. 340, No. 2 (Dec., 1993), pp. 587-594
DOI: 10.2307/2154667
Stable URL: http://www.jstor.org/stable/2154667
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Qualitative Uncertainty Principle for Unimodular Groups of Type I
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Abstract

It has long been known that if f ∈ L2(Rn) and the supports of f and its Fourier transform f̂ 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 f̂ have finite measure. These results may be thought of as qualitative uncertainty principles since they limit the "concentration" of the Fourier transform pair (f, f̂). 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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