Hilbert spaces of analytic functions with a contractive backward shift

@article{Aleman2019HilbertSO,
  title={Hilbert spaces of analytic functions with a contractive backward shift},
  author={Alexandru Aleman and Bartosz Malman},
  journal={Journal of Functional Analysis},
  year={2019}
}
View PDF on arXiv
9 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
1

9 Citations

Citation Type

Citation Type

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…
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…
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…
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…
Backward shift invariant subspaces in reproducing kernel Hilbert spaces
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme…
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…
The Cauchy dual subnormality problem via de Branges–Rovnyak spaces
The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a 2-isometry is subnormal. In this paper, we address this problem for cyclic 2-isometries. In view of some…
Higher order local Dirichlet integrals and de Branges-Rovnyak spaces
Invariant subspaces of the direct sum of forward and backward shifts on vector-valued Hardy spaces

References

SHOWING 1-10 OF 38 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…
Density of disk algebra functions in de Branges-Rovnyak spaces
Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces
In the theory of commutative Banach algebras with unit, an el- ement generates a dense ideal if and only if it is invertible, in which case its Gelfand transform has no zeros, and the ideal it…
Pick Interpolation and Hilbert Function Spaces
Prerequisites and notation Introduction Kernels and function spaces Hardy spaces $P^2(\mu)$ Pick redux Qualitative properties of the solution of the Pick problem in $H^\infty(\mathbb{D})$…
The Bergman Spaces
In this chapter we introduce the Bergman spaces and concentrate on the general aspects of these spaces. Most results are concerned with the Banach (or metric) space structure of Bergman spaces.…
Invariant subspaces of the Dirichlet shift.
Characterizing all invariant subspaces of an operator S on a Hubert space is a challenging problem. While it is open for most operators, it has been solved for U„9 the unilateral (unweighted) shift…
Harmonic Analysis of Operators on Hilbert Space
Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.-…
Reverse Carleson measures in Hardy spaces
We give a necessary and sufficient condition for a measure $$\mu $$μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li,…
de Branges-Rovnyak spaces: basics and theory
For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension…
Beurling's Theorem for the Bergman space
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…
...
...