# On model spaces and density of functions smooth on the boundary

@inproceedings{Limani2021OnMS, title={On model spaces and density of functions smooth on the boundary}, author={Adem Limani and Bartosz Malman}, year={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 the singular inner factor of Θ is concentrated on a countable union of BeurlingCarleson sets. In fact, we use a duality argument to show that if there exists a restriction of the associated singular measure which does not assign positive measure to Beurling-Carleson sets, then even larger classes of…

## 3 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…

A ug 2 02 1 ON THE PROBLEM OF SMOOTH APPROXIMATIONS IN DE BRANGES-ROVNYAK SPACES AND CONNECTIONS TO SUBNORMAL

- Mathematics
- 2021

For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H, we study the problem of approximation of a general function in H(b) by a function…

On the problem of smooth approximations in de Branges-Rovnyak spaces and connections to subnormal operators

- Mathematics
- 2021

For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H, we study the problem of approximation of a general function in H(b) by a function…

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