A lower bound in the tail law of the iterated logarithm for lacunary trigonometric series
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- by Santosh Ghimire and Charles N. Moore PDF
- Proc. Amer. Math. Soc. 142 (2014), 3207-3216 Request permission
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.References
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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
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3207-3216
- MSC (2010): Primary 42A55; Secondary 60F15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12055-7
- MathSciNet review: 3223376