On the asymptotic behavior of weakly lacunary series

Authors:
C. Aistleitner, I. Berkes and R. Tichy

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2505-2517

MSC (2010):
Primary 42A55, 42A61, 11D04, 60F05, 60F15

DOI:
https://doi.org/10.1090/S0002-9939-2011-10682-8

Published electronically:
February 9, 2011

MathSciNet review:
2784816

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a measurable function satisfying

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Additional Information

**C. Aistleitner**

Affiliation:
Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria

Email:
aistleitner@math.tugraz.at

**I. Berkes**

Affiliation:
Institute of Statistics, Graz University of Technology, Münzgrabenstraße 11, 8010 Graz, Austria

Email:
berkes@tugraz.at

**R. Tichy**

Affiliation:
Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria

Email:
tichy@tugraz.at

DOI:
https://doi.org/10.1090/S0002-9939-2011-10682-8

Keywords:
Lacunary series,
central limit theorem,
law of the iterated logarithm,
permutation-invariance,
Diophantine equations

Received by editor(s):
May 16, 2010

Received by editor(s) in revised form:
July 4, 2010

Published electronically:
February 9, 2011

Additional Notes:
The first author’s research was supported by FWF grant S9603-N23.

The second author’s research was supported by FWF grant S9603-N23 and OTKA grants K 67961 and K 81928.

The third author’s research was supported by FWF grant S9603-N23.

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.