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}
}
  • James W. Roberts
  • Published 1 March 1985
  • Mathematics
  • Illinois Journal of Mathematics
A ug 2 02 1 Inner functions , invariant subspaces and cyclicity in P t ( μ )-spaces
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
  • O. Ivrii
  • Mathematics
    Journal 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
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
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
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
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
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
  • O. Ivrii
  • Mathematics
    Trends 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
  • O. Ivrii
  • Mathematics
    Journal 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
We study the cyclicity in the Dirichlet type spaces for outer functions with zeros set is countable.
...
...