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Related papers: Multivariable operator-valued Nevanlinna-Pick inte…

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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…

Functional Analysis · Mathematics 2011-01-10 Kenneth R. Davidson , Ryan Hamilton

Our two principle goals are generalizations of the commutant lifting theorem and the Nevanlinna-Pick interpolation theorem to the context of Hardy algebras built from $W^*$-correspondences endowed with a sequence of weights. These theorems…

Operator Algebras · Mathematics 2016-08-18 Jennifer R Good

Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,\ldots, z_n\in \Omega$ and $w_1,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the $Pick\, interpolation\, problem$ asks when there is a…

Functional Analysis · Mathematics 2021-04-13 Tirthankar Bhattacharyya , Anindya Biswas , Vikramjeet Singh Chandel

In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…

Functional Analysis · Mathematics 2009-02-04 Gelu Popescu

The operator-valued Schur-class is defined to be the set of holomorphic functions $S$ mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator…

Classical Analysis and ODEs · Mathematics 2011-11-09 Joseph A. Ball , Animikh Biswas , Quanlei Fang , Sanne ter Horst

A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…

Functional Analysis · Mathematics 2007-05-23 Michael A. Dritschel , Stefania Marcantognini , Scott McCullough

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…

Complex Variables · Mathematics 2019-03-12 Anton Baranov , Rachid Zarouf

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…

Operator Algebras · Mathematics 2007-11-14 Kenneth R. Davidson , Vern I. Paulsen , Mrinal Raghupathi , Dinesh Singh

We explore the relationship between two noncommutative generalizations of the classical Nevanlinna-Pick theorem: one proved by Constantinescu and Johnson in 2003 and the other proved by Muhly and Solel in 2004. To make the comparison, we…

Operator Algebras · Mathematics 2016-07-15 Rachael M. Norton

Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,z_2,\ldots, z_n\in \Omega$ and $w_1,w_2,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the \textit{Pick interpolation problem} asks when there…

Functional Analysis · Mathematics 2023-09-13 Tirthankar Bhattacharyya , Anindya Biswas , Vikramjeet Singh Chandel

Nevanlinna-Pick interpolation and moment problems use the analytic structures provided by causality in order to provide rigorous bounds on smeared spectral functions. This proceedings discusses Nevanlinna-Pick interpolation and moment…

High Energy Physics - Lattice · Physics 2026-02-13 Ryan Abbott , William Jay , Patrick Oare

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…

Functional Analysis · Mathematics 2013-02-06 Michael T. Jury , Greg Knese , Scott McCullough

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…

Functional Analysis · Mathematics 2019-12-04 Deepak K. D. , Deepak Pradhan , Jaydeb Sarkar , Dan Timotin

The calculation of inclusive processes that involve the production of many particles is a challenge for lattice QCD, a Euclidean-space method that is far removed from real-time, multiparticle production. A new approach to this problem based…

High Energy Physics - Lattice · Physics 2026-05-19 Sarah Fields , Norman Christ

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…

Functional Analysis · Mathematics 2007-05-23 D. Alpay , T. Constantinescu , A. Dijksma , J. Rovnyak

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive…

Complex Variables · Mathematics 2013-08-13 Daniel Alpay , Vladimir Bolotnikov , Fabrizio Colombo , Irene Sabadini

Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the unit disk with the additional restriction that the interpolant…

Functional Analysis · Mathematics 2020-03-02 J. A. Ball , V. Bolotnikov , S. ter Horst

Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…

Functional Analysis · Mathematics 2022-05-30 Sanne ter Horst , Alma van der Merwe

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…

Optimization and Control · Mathematics 2020-03-02 J. A. Ball , S. ter Horst

Two different problems are considered here. First, a version of Schwarz-Pick Lemma for $n$ points leads to an interpolation problem for analytic functions from the disc into itself, which may be considered as a particular case of the…

Classical Analysis and ODEs · Mathematics 2014-07-30 Nacho Monreal Galan , Michael Papadimitrakis
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