Artículos (Análisis Matemático)https://hdl.handle.net/11441/108092019-08-26T08:11:31Z2019-08-26T08:11:31ZMonsters in Hardy and Bergman spaceshttps://hdl.handle.net/11441/875402019-06-21T08:06:20Z2002-01-01T00:00:00ZMonsters in Hardy and Bergman spaces
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In this paper the Hardy spaces Hp and the Bergman spaces Bp (1 ≤ p < ∞) on the
unit disk are considered, and it is shown that there are no Luh-monsters in them. Nevertheless, it is proved that T-monsters (as introduced by the authors in an earlier work) can be found in each of these spaces for any finite order linear differential operator T.
2002-01-01T00:00:00ZFamilies of strongly annular functions: linear structurehttps://hdl.handle.net/11441/875392019-06-21T07:58:07Z2013-01-01T00:00:00ZFamilies of strongly annular functions: linear structure
A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles in 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 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.
2013-01-01T00:00:00ZBackward Φ-shifts and universalityhttps://hdl.handle.net/11441/875382019-06-21T07:49:53Z2005-06-01T00:00:00ZBackward Φ-shifts and universality
In this paper we consider spaces of sequences which are valued in a topological space E and study generalized backward shifts associated to certain selfmappings of E. We characterize their universality in terms of dynamical properties of the underlying selfmappings. Applications to hypercyclicity theory are given. In particular, Rolewicz’s theorem on hypercyclicity of scalar multiples of the classical backward shift is extended.
2005-06-01T00:00:00ZInterpolation by hypercyclic functions for differential operatorshttps://hdl.handle.net/11441/875372019-06-21T07:41:04Z2009-04-01T00:00:00ZInterpolation by hypercyclic functions for differential operators
We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed
values at the points of the sequence and, simultaneously, having dense orbit in the space of holomorphic functions on Ω. The orbit is taken with respect to any fixed non-scalar differential operator generated by an entire function of subexponential type, thereby extending a recent result about MacLane-hypercyclicity due to Costakis, Vlachou and
Niess.
2009-04-01T00:00:00Z