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

      Professor Nicholas Young
      Senior Research Investigator

      • Telephone: +44 (0) 191 208 6479