Pseudo-Taylor expansions and the Carathéodory-Fejér problem (2012)

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

    Abstract: We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point x∈R and, a finite set of target values a0,a1,…,an∈C, to construct a function f in the Pick class such that the limit of f(k)(z)/k! as z→x nontangentially in the upper half-plane is ak for k=0,1,…,n. The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna.

      • Date: 06-08-2011
      • Journal: Journal of Mathematical Analysis and Applications
      • Volume: 386
      • Issue: 1
      • Pages: 308-318
      • Publisher: Academic Press
      • Publication type: Article
      • Bibliographic status: Published

      Keywords: Pick class; Boundary interpolation; Hankel matrix; Schur complement


      Dr Zinaida Lykova
      Reader in Pure Mathematics

      Professor Nicholas Young
      Senior Research Investigator

      • Telephone: +44 (0) 191 208 6479