On model spaces and density of functions smooth on the boundary

@article{Limani2022OnMS,
  title={On model spaces and density of functions smooth on the boundary},
  author={Adem Limani and Bartosz Malman},
  journal={Revista Matem{\'a}tica Iberoamericana},
  year={2022}
}
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… 
A ug 2 02 1 ON THE PROBLEM OF SMOOTH APPROXIMATIONS IN DE BRANGES-ROVNYAK SPACES AND CONNECTIONS TO SUBNORMAL
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
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
On the problem of smooth approximations in de Branges-Rovnyak spaces and connections to subnormal operators
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

References

SHOWING 1-10 OF 16 REFERENCES
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
Ideals in Rings of Analytic Functions with Smooth Boundary Values
Let A denote the Banach algebra of functions analytic in the open unit disc D and continuous in . If f and its first m derivatives belong to A, then the boundary function f(eiθ) belongs to Cm(∂D).
Sets of uniqueness for functions regular in the unit circle
the classical result being that of Fatou. However, very little is known about the properties of this boundary function F (0), and in particular about the sets E associated with the class C, having
Inner functions and cyclic vectors in the Bloch space
In this paper we construct a singular inner function whose polynomial multiples are dense in the little Bloch space qo . To do this we construct a singular measure on the unit circle with "best
Hankel operators, best approximations, and stationary Gaussian processes
CONTENTS Introduction Chapter I. Hankel operators and Toeplitz operators § 1.1. Hankel operators § 1.2. Toeplitz operators § 1.3. A connection between the Hankel operators and Chapter II. From
Multipliers and cyclic vectors in the Bloch space.
Holomorphic functions with infinitely differentiable boundary values
Hankel operators on the
...
...