Related papers: Nevanlinna-Pick interpolation for $C+BH^\infty$

Given a collection $K$ of positive integers, let $H^{\infty}_K(\mathbb{D})$ denote the set of all bounded analytic functions defined on the unit disk $\mathbb{D}$ in $\mathbb{C}$ whose $k^{\text{th}}$ derivative vanishes at zero, for all $k…

If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…

We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0)=0.$ Alternatively, these results can be interpreted as…

In this paper we characterize for 0 < p \leq \infty, the closed subspaces of Hp that are invariant under multiplication by all powers of a finite Blaschke factor B, except the first power. Our result clearly generalizes the invariant…

We study interpolation L-systems realizing finite Nevanlinna-Pick data sets and analyze their structural and quantitative characteristics. Explicit formulas are derived for the c-entropy and dissipation coefficient, two intrinsic invariants…

We consider a Nevanlinna-Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another…

We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record factorization results for pairs of nested invariant subspaces.

We extend Beurling's invariant subspace theorem, by characterizing subspaces $K$ of the noncommutative $L^p$ spaces which are invariant with respect to Arveson's maximal subdiagonal algebras, sometimes known as noncommutative $H^\infty$. It…

We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carath\'eodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting…

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…

This survey shows how, for the Nevanlinna class N of the unit disc, one can define and often characterize the analogues of well-known objects and properties related to the algebra of bounded analytic functions $ H^\infty$: interpolating…

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of…

The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the…

We revisit four approaches to the BiTangential Operator Argument Nevanlinna-Pick (BTOA-NP) interpolation theorem on the right half plane: (1) the state-space approach of Ball-Gohberg-Rodman, (2) the Fundamental Matrix Inequality approach of…

We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in…

Given an inner function $\theta$, the associated star-invariant subspace $K^\infty_\theta$ is formed by the functions $f\in H^\infty$ that annihilate (with respect to the usual pairing) the shift-invariant subspace $\theta H^1$ of the Hardy…

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider…

For a unital $C^*$-algebra $\mathcal A$ and a subspace $\mathcal B$ of $\mathcal A$, a characterization for a best approximation to an element of $\mathcal A$ in $\mathcal B$ is obtained. As an application, a formula for the distance of an…

Let $(X,\mu)$ be a space with a finite measure $\mu$, let $A$ and $B$ be $w^*$-closed subalgebras of $L^{\infty}(\mu)$, and let $C$ and $D$ be closed subspaces of $L^p(\mu)$ ($1<p<\infty$) that are modules over $A$ and $B$, respectively.…

There are three new things in this paper about the open symmetrized bidisk $\mathbb G = \{(z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. They are motivated in the Introduction. In this Abstract, we mention them in the order in which they will be…