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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Gaussian law and the law of the iterated logarithm for lacunary sets of characters
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by E. Dudley PDF
Trans. Amer. Math. Soc. 214 (1975), 187-214 Request permission

Abstract:

Salem and Zygmund showed that the Gaussian law holds for Hadamard sequences of real numbers while Mary Weiss proved a similar result for the law of the iterated logarithm. In the present paper, the author obtains corresponding results for lacunary sets of characters of an arbitrary infinite compact abelian group. It is shown that the laws are best satisfied for a certain class of lacunary sets but that modified results apply to more general classes.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 187-214
  • MSC: Primary 42A44; Secondary 43A46, 60F15
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0380246-1
  • MathSciNet review: 0380246