The boundary Carathéodory–Fejér interpolation problem

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  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
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.
PublisherAcademic Press
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