# The boundary Carathéodory–Fejér interpolation problem

1. Lookup NU author(s)
2. Professor Jim Agler
3. Dr Zinaida Lykova
4. Professor Nicholas Young
Author(s)Agler J, Lykova ZA, Young NJ
Publication type Article
JournalJournal of Mathematical Analysis and Applications
Year2011
Volume382
Issue2
Pages645-662
ISSN (print)0022-247X
ISSN (electronic)1096-0813
Full text is available for this publication:
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.