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A lower bound in the tail law of the iterated logarithm for lacunary trigonometric series


Authors: Santosh Ghimire and Charles N. Moore
Journal: Proc. Amer. Math. Soc. 142 (2014), 3207-3216
MSC (2010): Primary 42A55; Secondary 60F15
Published electronically: June 2, 2014
MathSciNet review: 3223376
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Abstract: Salem and Zygmund obtained an upper bound for a tail law of the iterated logarithm for sums of the form $ \sum _{k=N}^{\infty } a_{k} \cos (n_{k}x)+b_k \sin (n_{k}x)$, where $ n_{k}$ satisfies a Hadamard gap condition and $ \sum _{k=1}^{\infty } a_k^2 + b_k^2 < \infty .$ Here we obtain a lower bound in their result under the same hypotheses.


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Additional Information

Santosh Ghimire
Affiliation: Department of Science and Humanities, Tribhuvan University, Pulchowk Campus, Lalitpur, Kathmandu, Nepal
Email: ghimire@math.ksu.edu

Charles N. Moore
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Address at time of publication: Department of Mathematics, Washington State University, Pullman, Washington 99164
Email: cnmoore@math.wsu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12055-7
Keywords: Law of the iterated logarithm, lacunary trigonometric series
Received by editor(s): May 21, 2012
Received by editor(s) in revised form: October 8, 2012
Published electronically: June 2, 2014
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.