Large subspaces of compositionally universal functions with maximal cluster sets

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

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

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

关键词: Universal functions;    Hypercyclic vectors;    Composition operators;    Maximal cluster set;    Dense-lineability;    Spaceability;   

DOI  :  10.1016/j.jat.2011.10.005

来源: Elsevier

【 摘 要 】

Let (phi n) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (con), we construct an H(G)-dense linear manifold as well as a closed infinite-dimensional linear manifold all of whose non-zero functions have H(G)-dense orbits under the action of a sequence of composition operators associated with (phi n). Simultaneously, these functions also present maximal cluster sets along each member of a large class of curves in G tending to the boundary. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free