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The central limit theorem for lacunary series


Authors: Katusi Fukuyama and Shigeru Takahashi
Journal: Proc. Amer. Math. Soc. 127 (1999), 599-608
MSC (1991): Primary 60F05, 42A55
DOI: https://doi.org/10.1090/S0002-9939-99-04541-4
MathSciNet review: 1468191
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Abstract: In this paper, the central limit theorem for lacunary trigonometric series is proved. Two gap conditions by Erdos and Takahashi are extended and unified. The criterion for the Fourier character of lacunary series is also given.


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Katusi Fukuyama
Affiliation: Department of Mathematics, Kobe University, Rokko, Kobe, 657 Japan
Email: fukuyama@math.s.kobe-u.ac.jp

Shigeru Takahashi
Affiliation: Yamamichi-cho 21-1-601, Hirosaki, 036 Japan

DOI: https://doi.org/10.1090/S0002-9939-99-04541-4
Keywords: Lacunary series, central limit theorem, Fourier series, Fourier Stieltjes series
Received by editor(s): January 27, 1997
Received by editor(s) in revised form: May 23, 1997
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1999 American Mathematical Society