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

 

The convergence of the Fourier integral
of a unimodal distribution


Author: Constantine Georgakis
Journal: Proc. Amer. Math. Soc. 126 (1998), 3239-3241
MSC (1991): Primary 42A38; Secondary 60E10
MathSciNet review: 1452804
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Abstract: 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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04385-8
PII: S 0002-9939(98)04385-8
Keywords: Khintchine, unimodal distribution, Fourier integral, inversion, characteristic function
Received by editor(s): December 14, 1994
Received by editor(s) in revised form: March 10, 1997
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society