### The boundary Carathéodory–Fejér interpolation problem (2011)

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

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.

• Date: 29-04-2011
• Journal: Journal of Mathematical Analysis and Applications
• Volume: 382
• Issue: 2
• Pages: 645-662
• Publisher: Academic Press
• Publication type: Article
• Bibliographic status: Published

Keywords: Pick class, boundary interpolation, parametrization, Hankel matrix, Schur complement.

 Dr Zinaida Lykova Reader in Pure Mathematics Email: zinaida.lykova@ncl.ac.uk Telephone: +44 (0) 191 208 6479 Professor Nicholas Young Senior Research Investigator Telephone: +44 (0) 191 208 6479