Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 135-148

ON THE RANGE OF ∑_n=1^∞ ±c_n

Xing-Gang He and Chun-Tai Liu

Central China Normal University, School of Mathematics and Statistics
Wuhan, 430079, P.R. China; xingganghe 'at' 163.com, xingganghe 'at' sina.com

Wuhan Polytechnic University, School of Mathematics and Computer Science
Wuhan, 430023, P.R. China; lct984 'at' 163.com

Abstract. Let {c_n}_n=1^∞ be a sequence of complex numbers. In this paper we answer when the range of ∑_n=1^∞ ±c_n is dense or equal to the complex plane. Some examples are given to explain our results. As its application, we calculate the Hausdorff dimension of the level sets of a Rademacher series with complex coefficients.

2010 Mathematics Subject Classification: Primary 28A78, 40A05, 42C10.

Key words: Hausdorff dimension, infinite Bernoulli convolution, Moran function system, Rademacher series.

Reference to this article: X.-G. He and C.-T. Liu: On the range of ∑_n=1^∞ ±c_n. Ann. Acad. Sci. Fenn. Math. 40 (2015), 135-148.

Full document as PDF file

doi:10.5186/aasfm.2015.4004

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