The boundary Caratheodory-Fejer interpolation problem

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:382

Article

Agler, Jim²  Lykova, Zinaida A.¹  Young, N. J.³ 

[1] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

[2] Univ Calif San Diego, Dept Math, San Diego, CA 92103 USA

[3] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Pick class;    Boundary interpolation;    Parametrization;    Hankel matrix;    Schur complement;   

DOI  :  10.1016/j.jmaa.2011.04.071

来源: Elsevier

【 摘 要 】

We give a new solvability criterion for the boundary Caratheodory-Fejer problem: given a point x epsilon R and, a finite set of target values, to construct a function f in the Pick class such that the first few derivatives of f take on the prescribed target values at x. We also derive a linear fractional parametrization of the set of solutions of the interpolation problem with real target values. The proofs are based on a reduction method due to Julia and Nevanlinna. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free