Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T23:39:50.407Z Has data issue: false hasContentIssue false
  • English
  • Français

The central limit theorem for trigonometric series

Published online by Cambridge University Press:  22 January 2016

Takafumi Murai
Takafumi Murai*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We denote by Z+ the semi-group of positive integers. For a subset E of Z+, we denote by |E| (≦ + ∞) its cardinal number and by E(n) the intersection of E and an interval [1, n) (n ≧ 1). We shall identify a subset E of Z+ with a sequence, arranging elements of E according to their order.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 87 , November 1982 , pp. 79 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Berkes, L., On the central limit theorem for lacunary trigonometric series, Anal. Math., 4 (1978), 159–180.Google Scholar
[2] Erdös, P., On trigonometric sums with gaps, Magyar Tud. Acad. Kutato Int. Közl., 7 (1962), 37–42.Google Scholar
[3] Kahane, J. P., Lacunary Taylor and Fourier series, Bull Amer. M. S., 70 (1964), 199–213.Google Scholar
[4] Takahashi, S., Probability limit theorems for trigonometric series, Colloquia Mathematica S. 11, Limit theorems of probability theory, Keszthely (Hungary), 1974, 381–397 (Edited by Révész, P.).Google Scholar
[5] Zygmund, A., Trigonometric series II, Cambridge Univ. Press, 1959.Google Scholar