A dynamical characterization of sub-Arakelian subsets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Calderon-Moreno, M. C.¹  Prado-Bassas, J. A.¹ 

[1] Fac Matemat, Dept Anal Matemat, Seville 41080, Spain

关键词: Universal functions;    Sub-Arakelian subsets;    Similarities;    Dense-lineability;    Spaceability;   

DOI  :  10.1016/j.jmaa.2013.04.023

来源: Elsevier

【 摘 要 】

We are going to characterize those sets which can be covered by an Arakelian set in terms of dynamical properties of entire functions via similarities. Moreover, if we consider the set of universal entire functions via similarities that are bounded on such a sub-Arakelian set, then it is shown that its algebraic size is as large as possible. As a consequence, we prove that the set of universal entire functions bounded on every (straight) line is algebraically large. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free