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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a theorem of Paley and Wiener


Author: Richard T. Miller
Journal: Proc. Amer. Math. Soc. 113 (1991), 643-649
MSC: Primary 42A38
MathSciNet review: 1070522
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Abstract: A famous theorem of Paley and Wiener gives necessary and sufficient conditions for a function to be the amplitude of the Fourier transform of a function that vanishes on the negative real line. We find similar conditions sufficient to conclude that the inverse transform decays exponentially at minus infinity.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1070522-6
PII: S 0002-9939(1991)1070522-6
Article copyright: © Copyright 1991 American Mathematical Society