# Density of disk algebra functions in de Branges-Rovnyak spaces

@article{Aleman2017DensityOD,
title={Density of disk algebra functions in de Branges-Rovnyak spaces},
author={Alexandru Aleman and Bartosz Malman},
journal={Comptes Rendus Mathematique},
year={2017},
volume={355},
pages={871-875}
}
• Published 6 April 2017
• Mathematics
• Comptes Rendus Mathematique
10 Citations
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
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
Construction of some smooth Cauchy transforms
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
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
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
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
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
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

## References

SHOWING 1-10 OF 10 REFERENCES
Sub-Hardy Hilbert Spaces in the Unit Disk
Hilbert Spaces Inside Hilbert Spaces. Hilbert Spaces Inside H 2 . Cauchy Integral Representations. Nonextreme Points. Extreme Points. Angular Derivatives. Higher Derivatives. Equality of H(b) and
Theory of linear operations
• S. Banach
• Mathematics
North-Holland mathematical library
• 1987
The Lebesgue-Stieltjes Integral is used as a model for Banach Spaces to study the topological structure of Linear Metric Spaces and the properties of these Spaces are compared to those of Hilbert Spaces.
Constructive Approximation in de Branges–Rovnyak Spaces
• Mathematics
• 2015
In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function f can be approximated in norm by its dilates $$f_r(z):=f(rz)~(r<1)$$fr(z):=f(rz)(r<1). We
Beurling's Theorem for the Bergman space
• Mathematics
• 1996
A celebrated theorem in operator theory is A. Beurling's description of the invariant subspaces in $H^2$ in terms of inner functions [Acta Math. {\bf81} (1949), 239--255; MR0027954 (10,381e)]. To do
The Cauchy Transform
• Mathematics
• 2006
Overview Preliminaries The Cauchy transform as a function The Cauchy transform as an operator Topologies on the space of Cauchy transforms Which functions are Cauchy integrals? Multipliers and
The Uncertainty Principle in Harmonic Analysis
The Uncertainty Principle (up) as understood in this lecture is the following informal assertion: a non-zero “object” (a function, distribution, hyperfunction) and its Fourier image cannot be too
The Hardy Space Of A Slit Domain
The the hardy space of a slit domain is universally compatible with any devices to read and is available in the authors' digital library an online access to it is set as public so you can download it instantly.
Some open problems in complex and harmonic analysis: report on problem session held during the conference Completeness problems
• Carleson measures, and spaces of analytic functions, in Recent progress on operator theory and approximation in spaces of analytic functions, vol. 679 of Contemp. Math., Amer. Math. Soc., Providence, RI
• 2016
Invariant subspaces of shift operators . An axiomatic approach , Zap . Nauchn . Sem . Leningrad . Otdel
• The Hardy space of a slit domain , Frontiers in Mathematics
• 1981