Related papers: Interpolation and sampling for analytic selfmappin…
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 prove a version of the Schwarz lemma for holomorphic mappings from the unit disk into the symmetric product of a Riemann surface. Our proof is function-theoretic and self-contained. The main novelty in our proof is the use of the…
We analyse two special cases of $\mu$-synthesis problems which can be reduced to interpolation problems in the set of analytic functions from the disc into the symmetrised bidisc and into the tetrablock. For these inhomogeneous domains we…
We analyze the three point Pick interpolation problem on the bidisk
We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with…
We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in $\mathbb{C}^d$.
The most classical version of the Schwarz lemma involves the behavior at the origin of a bounded, holomorphic function on the disc. Pick's version of the Schwarz lemma allows one to move the origin to other points of the disc. In the…
Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
We give a solution to Pick's interpolation problem on the unit polydisc in $\mathbb{C}^n$, $n\geq 2$, by characterizing all interpolation data that admit a $\mathbb{D}$-valued interpolant, in terms of a family of positive-definite kernels…
The nondegenerate Nevanlinna-Pick-Carath\'eodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class $\cS_\kappa$ for every $\kappa\ge \kappa_{\rm min}$…
The aim of this paper is to establish some properties of solutions to the Dirichlet-Neumann problem: $(\partial_z\partial_{\overline{z}})^2 w=g$ in the unit disc $\ID$, $w=\gamma_0$ and…
In this article we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that…
We construct automorphisms of $\C^n$ which map certain discrete sequences one onto another with prescribed finite jet at each point, thus solving a general Mittag-Leffler interpolation problem for automorphisms. Under certain circumstances,…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for…
The Nevanlinna-Pick problem and the simplest case of the Carath\'eodory-Fej\'er problem on the spectral ball $\Om_3$ are reduced to interpolation problems on the symmetrized three-disc $\G_3.$
An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for…
The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a…
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…