Related papers: Interpolation in multivariable de Branges-Rovnyak …
In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative…
We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…
We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras 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…
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…
We develop a $d$-variable analog of the two-component de Bran-ges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in…
This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over…
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.
Motivated by recent applications of weighted norm inequalities to maximal regularity of first and second order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted…
An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers for the reproducing kernel Hilbert space ${\mathcal H}(k_{d})$ on the unit ball ${\mathbb B}^{d}…
We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities.
The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give…
Using the notion of commutative operator vessels, this work investigates de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. As a special case,…
We study the interpolation sets for the Hardy-Sobolev spaces defined on the unit ball of ${\bf C}^n$. We begin by giving a natural extension to ${\bf C}^n$ of the condition that is known to be necessay and sufficient for interpolation sets…
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 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…
In this paper, we study the de Branges-Rovnyak spaces $\mathcal{H}(B)$ generated by row Schur functions $B$ with mate $a$. We prove that the polynomials are dense in $\mathcal{H}(B)$, and characterize the backward shift invariant subspaces…
We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\mathbb{C} ^d$. Here, the full Fock space is identified…
We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for…
We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities…