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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The convergence of the Fourier integral of a unimodal distribution
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by Constantine Georgakis PDF
Proc. Amer. Math. Soc. 126 (1998), 3239-3241 Request permission


We show that the characteristic function of a unimodal probability distribution function can be inverted by the Fourier transform a.e. if and only if the distribution is absolutely continuous. The result complements Khintchine’s criterion for unimodal distributions.
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Additional Information
  • Constantine Georgakis
  • Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
  • Received by editor(s): December 14, 1994
  • Received by editor(s) in revised form: March 10, 1997
  • Communicated by: J. Marshall Ash
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3239-3241
  • MSC (1991): Primary 42A38; Secondary 60E10
  • DOI:
  • MathSciNet review: 1452804