On the class of limits of lacunary trigonometric series
 C. Aistleitner
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Let (n _{ k })_{ k≧1} be a lacunary sequence of positive integers, i.e. a sequence satisfying n _{ k+1}/n _{ k } > q > 1, k ≧ 1, and let f be a “nice” 1periodic function with ∝ _{0} ^{1} f(x) dx = 0. Then the probabilistic behavior of the system (f(n _{ k } x))_{ k≧1} is very similar to the behavior of sequences of i.i.d. random variables. For example, Erdős and Gál proved in 1955 the following law of the iterated logarithm (LIL) for f(x) = cos 2πx and lacunary \( (n_k )_{k \geqq 1} \) :
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 Title
 On the class of limits of lacunary trigonometric series
 Journal

Acta Mathematica Hungarica
Volume 129, Issue 12 , pp 123
 Cover Date
 20101001
 DOI
 10.1007/s1047401092183
 Print ISSN
 02365294
 Online ISSN
 15882632
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 lacunary series
 law of the iterated logarithm
 primary 11K38, 42A55, 60F15
 Authors

 C. Aistleitner ^{(1)}
 Author Affiliations

 1. Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria