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Lookup NU author(s): Professor Jim Agler, Dr Zinaida LykovaORCiD, Professor Nicholas Young
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
Publisher: Academic Press
URL: http://dx.doi.org/10.1016/j.jmaa.2011.04.071
DOI: 10.1016/j.jmaa.2011.04.071
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