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Related papers: Lifting to the spectral ball with interpolation

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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 $\G_3.$

Complex Variables · Mathematics 2012-09-03 Nikolai Nikolov , Peter Pflug , Pascal J. Thomas

The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting…

Functional Analysis · Mathematics 2025-09-09 Deepak K. D. , Jaydeb Sarkar

We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.

Complex Variables · Mathematics 2016-04-14 Łukasz Kosiński , Włodzimierz Zwonek

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

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

The spectral unit ball $\Omega_n$ is the set of all $n\times n$ matrices with spectral radius less than $1$. Let $\pi(M) \in \mathbb C^n$ stand for the coefficients of its characteristic polynomial of $M$ (up to signs), i.e. the elementary…

Complex Variables · Mathematics 2017-10-24 Nikolai Nikolov , Pascal J. Thomas , Duc-Anh Tran

It is very elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are just left inverses to complex geodesics. In the present article we show that the same property holds for a three-point Pick…

Complex Variables · Mathematics 2015-03-12 Lukasz Kosinski

The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna- Pick interpolation problem assuming the associated Pick operator is strictly positive. The…

Functional Analysis · Mathematics 2018-04-24 A. E. Frazho , S. Ter Horst , M. A. Kaashoek

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

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

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

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

Nevanlinna-Pick interpolation problem has been widely studied in recent decades, however, the known algorithm is not simplistic and robust enough. This paper provide a new method to solve the Nevanlinna-Pick interpolation problem with…

Numerical Analysis · Mathematics 2024-05-27 Cui Yufang

We introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective…

Complex Variables · Mathematics 2007-05-23 Gautam Bharali

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

We give an elementary proof of Sarason's solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The…

Complex Variables · Mathematics 2010-11-09 Jim Agler , N. J. Young

We formulate three boundary Nevanlinna-Pick interpolation problems for generalized Nevanlinna functions. For each problem, we parameterize the set of all solutions in terms of a linear fractional transformation with an extended Nevanlinna…

Complex Variables · Mathematics 2007-05-23 Paul Anthony Smith

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

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

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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