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On a theorem of Paley and Wiener


Author: Richard T. Miller
Journal: Proc. Amer. Math. Soc. 113 (1991), 643-649
MSC: Primary 42A38
DOI: https://doi.org/10.1090/S0002-9939-1991-1070522-6
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.


References [Enhancements On Off] (What's this?)

  • [1] Henry Helson, Harmonic analysis, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. MR 729682
  • [2] Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142

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DOI: https://doi.org/10.1090/S0002-9939-1991-1070522-6
Article copyright: © Copyright 1991 American Mathematical Society