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The central limit theorem for lacunary series
Author(s):
Katusi
Fukuyama;
Shigeru
Takahashi
Journal:
Proc. Amer. Math. Soc.
127
(1999),
599-608.
MSC (1991):
Primary 60F05, 42A55
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.
References:
- 1.
- P. Erd\H{o}s, On trigonometric series with gaps, Magyar Tud. Akad. Mat. Kutato Int. Közl. 7 (1962), 37-42. MR 26:2797
- 2.
- W. Feller, An introduction to probability theory and its applications vol. II, second ed., Wiley, New York, 1971. MR 42:5292
- 3.
- A. N. Kolmogorov, Une contribution à l'étude de la convergence des séries de Fourier, Fund. Math. 5 (1924), 26-27.
- 4.
- R. Salem & A. Zygmund, On lacunary trigonometric series, Proc. Nat. Acad. Sci. 33 (1947), 333-338. MR 9:181d
- 5.
- S. Takahashi, A version of the central limit theorem for trigonometric series, Tôhoku Math. J. 16 (1964), 384-398. MR 30:4114
- 6.
- -, On trigonometric series with gaps, Tôhoku Math. J. 17 (1965), 227-234. MR 32:4459
- 7.
- -, On lacunary trigonometric series, Proc. Japan Acad. 41 (1965), 503-506. MR 33:4564
- 8.
- -, On the lacunary Fourier series, Tôhoku Math. J. 19 (1967), 79-85. MR 35:2067
- 9.
- -, On lacunary trigonometric series II, Proc. Japan Acad. 44 (1968), 766-770. MR 39:4583
- 10.
- A. Zygmund, On the convergence of lacunary trigonometric series, Fund. Math. 16 (1930), 90-97; Correction, Fund. Math. 18 (1932), 312.
- 11.
- -, Trigonometric series vol. I, second ed., Cambridge Univ. Press, Cambridge, (1959). MR 21:6498
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Additional Information:
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:
10.1090/S0002-9939-99-04541-4
PII:
S 0002-9939(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
Copyright of article:
Copyright
1999,
American Mathematical Society
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