arXiv subjects

J. López-Salazar

Publications and source records attributed to J. López-Salazar.

3 recordsLinked to original sources

arXiv2025

Spaceability of special families of null sequences of holomorphic functions

In this note, we consider the space $H(Ω)^{\mathbb N}$ of sequences of holomorphic functions on an open set $Ω\subset {\mathbb C}$. If $H(Ω)$ is endowed with its natural topology and $H(Ω)^{\mathbb N}$ is endowed with the product topology, then it is proved the existence of two closed infinite dimensional vector subspaces of $H(Ω)^{\mathbb N}$ such that all nonzero members of the first subspace are sequences tending to zero pointwisely but not compactly on $Ω$ and all nonzero members of the second subspace are sequences tending to zero compactly but not uniformly on $Ω$. This complements the results provided in a recent work by the same authors.

math.CV↗

arXiv2024

Modes of convergence of sequences of holomorphic functions: a linear point of view

In this paper, pointwise convergence, uniform convergence and compact convergence of sequences of holomorphic functions on an open subset of the complex plane are compared from a linear point of view. In fact, it is proved the existence of large linear algebras consisting, except for zero, of sequences of holomorphic functions tending to zero compactly but not uniformly on the open set or of sequences of holomorphic functions tending pointwisely to zero but not compactly. Also dense linear subspaces in an appropriate Fréchet space as well as infinite dimensional Banach spaces of sequences converging to zero in the mentioned modes are shown to exist.

math.CV↗

arXiv2024

Hypercyclic subspaces for sequences of finite order differential operators

It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense $\mathfrak{c}$-dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence $(P_n(D))$ of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercylic function.

math.CV↗