# ePrints

## The boundary Carathéodory–Fejér interpolation problem

Lookup NU author(s): Professor Jim Agler, Dr Zinaida LykovaORCiD, Professor Nicholas Young

### Abstract

We give an elementary proof of a solvability criterion for the {\em boundary Carath\'{e}odory-Fej\'{e}r problem}: given a point $x \in \R$ 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. The proofs are based on a reduction method due to Julia and Nevanlinna.

Author(s): Agler J, Lykova ZA, Young NJ

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Analysis and Applications

Year: 2011

Volume: 382

Issue: 2

Pages: 645-662

Print publication date: 29/04/2011

Date deposited: 08/11/2010

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

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### Funding

Funder referenceFunder name
4918London Mathematical Society
EP/G000018/1EPSRC
DMS 0801259National Science Foundation