# Cyclic inner functions in the Bergman spaces and weak outer functions in $H^{p}$, $0 < p <1$

@article{Roberts1985CyclicIF, title={Cyclic inner functions in the Bergman spaces and weak outer functions in \$H^\{p\}\$, \$0 < p <1\$}, author={James W. Roberts}, journal={Illinois Journal of Mathematics}, year={1985}, volume={29}, pages={25-38} }

## 31 Citations

A ug 2 02 1 Inner functions , invariant subspaces and cyclicity in P t ( μ )-spaces

- Mathematics
- 2021

We study the invariant subspaces generated by inner functions for a class of Pt(μ)-spaces which can be identified as spaces of analytic functions in the unit disk D, where μ is a measure supported in…

Prescribing inner parts of derivatives of inner functions

- MathematicsJournal d'Analyse Mathématique
- 2019

Let $\mathscr J$ be the set of inner functions whose derivatives lie in Nevanlinna class. In this note, we show that the natural map $F \to \text{Inn}(F'): \mathscr J/\text{Aut}(\mathbb{D}) \to…

On model spaces and density of functions regular on the boundary

- Mathematics
- 2021

We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It turns out that such approximation is possible if and only if the singular measure associated to…

On model spaces and density of functions smooth on the boundary

- Mathematics
- 2021

We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to…

Cyclic inner functions in growth classes and applications to approximation problems

- Mathematics
- 2022

It is well-known that for any inner function θ deﬁned in the unit disk D the following two conditons: ( i ) there exists a sequence of polynomials { p n } n such that lim n →∞ θ ( z ) p n ( z ) = 1…

Constructions of some families of smooth Cauchy transforms

- Mathematics
- 2021

For a given Beurling-Carleson subset E of the unit circle T which has positive Lebesgue measure, we give explicit formulas for measurable functions supported on E such that their Cauchy transforms…

An abstract approach to approximations in spaces of pseudocontinuable functions

- Mathematics
- 2021

We give an abstract approach to approximations with a wide range of regularity classes X in spaces of pseudocontinuable functions K p θ, where θ is an inner function and p > 0. More precisely, we…

Describing Blaschke Products by Their Critical Points

- MathematicsTrends in Mathematics
- 2021

In this talk, I will discuss a question which originates in complex analysis but is really a problem in non-linear elliptic PDE. A finite Blaschke product is a proper holomorphic self-map of the unit…

Stable convergence of inner functions

- MathematicsJournal of the London Mathematical Society
- 2020

Let J be the set of inner functions whose derivative lies in the Nevanlinna class. In this paper, we discuss a natural topology on J where Fn→F if the critical structures of Fn converge to the…

Cyclicity in Dirichlet type spaces

- Mathematics
- 2018

We study the cyclicity in the Dirichlet type spaces for outer functions with zeros set is countable.