Related papers: On the coefficient formula for de Branges-Rovnyak …

In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates $f\_r(z):=f(rz)~(r \textless{} 1)$. We show that this is \emph{not} the case for the de…

We describe de Branges-Rovnyak spaces $\mathcal H (b_{\alpha})$, $\alpha>0$, where the function $b_{\alpha}$ is not extreme in the unit ball of $H^{\infty}$ on the unit disk $\mathbb D$, defined by the equality…

For the class of de Branges-Rovnyak spaces $\mathcal{H}(b)$ of the unit disk $\mathbb{D}$ defined by extreme points $b$ of the unit ball of $H^\infty$, we study the problem of approximation of a general function in $\mathcal{H}(b)$ by a…

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 $f_r(z):=f(rz)~(r<1)$, in other words, $\lim_{r\to1^-}\|f_r-f\|=0$. We construct a…

Let $\mathcal{H}(b)$ denote the de Branges--Rovnyak space associated with a function $b$ in the unit ball of $H^\infty(\mathbb{C}_+)$. We study the boundary behavior of the derivatives of functions in $\mathcal{H}(b)$ and obtain weighted…

We study conditions for containment of a given space $X$ of analytic functions on the unit disk $\mathbb{D}$ in the de Branges-Rovnyak space $\mathcal{H}(b)$. We deal with the non-extreme case in which $b$ admits a Pythagorean mate $a$, and…

In this paper we give an explicit description of de Branges-Rovnyak spaces $\HH(b)$ when $b$ is of the form $q^{r}$, where $q$ is a rational outer function in the closed unit ball of $H^{\infty}$ and $r$ is a positive number.

We show that there exists a de Branges-Rovnyak space $\mathcal{H}(b)$ on the unit disk containing a function $f$ with the following property: even though $f$ can be approximated by polynomials in $\mathcal{H}(b)$, neither the Taylor partial…

Motivated by the recent developments of de Branges-Rovnyak spaces, we investigate the function theoretic aspects of finite rank de Branges-Rovnyak spaces $H(B)$ generated by row-valued Schur functions $B$. We provide a generalization of…

In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges--Rovnyak spaces $\HH(b)$, where $b$ is in the unit ball of $H^\infty(\CC_+)$. In particular, we generalize a result of…

For $b\in H^\infty_1$, the closed unit ball of $H^\infty$, the de Branges-Rovnyak spaces $\mathcal{H}(b)$ is a Hilbert space contractively contained in the Hardy space $H^2$ that is invariant by the backward shift operator $S^*$. We…

The de Branges--Rovnyak spaces are known to provide an alternate functional model for contractions on a Hilbert space, equivalent to the Sz.-Nagy--Foias model. The scalar de Branges--Rovnyak spaces $\mathcal{H}(b)$ have essentially…

In the framework of Sobolev (Bessel potential) spaces $H^n(\reali^d, \reali {or} \complessi)$, we consider the nonlinear Nemytskij operator sending a function $x \in \reali^d \mapsto f(x)$ into a composite function $x \in \reali^d \mapsto…

Let $B_n$ denote the unit ball of $\mathbb{C}^n$, $n\ge 1$, and let $\mathcal{D}$ denote a finite product of $B_{n_j}$, $j\ge 1$. Given a non-constant holomorphic function $b: \mathcal{D} \to B_1$, we study the corresponding family…

We discuss de Branges-Rovnyak spaces $\mathcal H(b)$ generated by nonextreme and rational functions $b$ and local Dirichlet spaces of order $m$ introduced in [6]. In [6] the authors characterized nonextreme $b$ for which the operator…

In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal H(b)$, where the symbol $b$ is a rational function in the unit ball of $H^\infty$ that is…

We consider normalized univalent functions with prescribed second Taylor coefficient $a_2$. For convex functions $f$ we study the Hardy spaces to which $f$ and $f'$ belong, refining in particular on a theorem of Eenigenburg and Keogh, and…

A Hilbert point in $H^p(\mathbb{T}^d)$, for $d\geq1$ and $1\leq p \leq \infty$, is a nontrivial function $\varphi$ in $H^p(\mathbb{T}^d)$ such that $\| \varphi \|_{H^p(\mathbb{T}^d)} \leq \|\varphi + f\|_{H^p(\mathbb{T}^d)}$ whenever $f$ is…

For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…

Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the…