## 27 Citations

Peak sets and boundary interpolation sets for the unit disc: a survey

- MathematicsBulletin of the London Mathematical Society
- 2020

This paper surveys results concerning peak sets and boundary interpolation sets for the unit disc. It includes hitherto unpublished results proved by Ullrich on peak sets for the Zygmund class.

Construction of some smooth Cauchy transforms

- Mathematics
- 2021

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

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…

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…

Algebras on Surfaces

- Mathematics
- 2015

The first part of the paper is devoted to algebras on one-dimensional varieties in $\mathsf{C}^n$ that are bounded by finite unions of mutually disjoint rectifiable simple closed curves. The relevant…

Restriction spaces of A ∞

- Mathematics
- 2013

In the present paper it is shown that for certain totally disconnected Carleson sets E the restriction space A∞(E) = {f |E : f ∈ A∞} has a basis. Its isomorphism type is determined. The result…

Admissible functions for the Dirichlet space

- Mathematics
- 2010

Zero sets and uniqueness sets of the classical Dirichlet space D are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to…

Sets of uniqueness for the Gevrey classes

- Mathematics
- 2006

Definition. A compact subset E of the real line R is said tO be a set of uniqueness for G~ if there is no nonzero function f , fEG~, that vanishes on E together with all its derivatives. The system…

Contemporary Mathematics The classical Dirichlet space

- Mathematics
- 2005

D |f ′|2 dx dy. In particular, we will cover the basic structure of these functions their boundary values and their zeros along with two important operators that act on this space of functions the…