naa a22 4500 510760724 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0080-9 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0080-9 Families of strongly annular functions: linear structure [Elektronische Daten] [Luis Bernal-González, Antonio Bonilla] A function f holomorphic in the unit disk $\mathbb{D}$ is called strongly annular if there exists a sequence of concentric circles in $\mathbb{D}$ expanding out to the unit circle such that f goes to infinity as |z| goes to 1 through these circles. The residuality of the family of strongly annular functions in the space of holomorphic functions on $\mathbb{D}$ is well known, and it is extended here to certain classes of functions. This important topological property is enriched in this paper by studying algebraic-topological properties of the mentioned family, in the modern setting of lineability. Namely, we prove that although this family is clearly nonlinear, it contains, except for the zero function, large vector subspaces as well as infinitely generated algebras. Similar results are obtained for strongly annular functions on the whole complex plane and for weighted Bergman spaces. Revista Matemática Complutense, 2011 Strongly annular functions nationallicence Entire functions nationallicence Dense-lineability nationallicence Algebrability nationallicence Bergman spaces nationallicence Bernal-González Luis Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, 41080, Sevilla, Spain aut Bonilla Antonio Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de La Laguna, C/Astrofísico Francisco Sánchez, 38271, La Laguna, Tenerife, Spain aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 283-297 1139-1138 26:1<283 2013 26 13163 https://doi.org/10.1007/s13163-011-0080-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0080-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bernal-González Luis Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, 41080, Sevilla, Spain aut NATIONALLICENCE 700 1- Bonilla Antonio Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de La Laguna, C/Astrofísico Francisco Sánchez, 38271, La Laguna, Tenerife, Spain aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 283-297 1139-1138 26:1<283 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer