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On the range of $\sum_{n=1}^\infty\pm c_n$
- Publication Year :
- 2013
-
Abstract
- Let $\{c_n\}_{n=1}^\infty$ be a sequence of complex numbers. In this paper we answer when the range of $\sum_{n=1}^\infty\pm c_n$ 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.<br />Comment: 15 pages
- Subjects :
- Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1309.7745
- Document Type :
- Working Paper