Pseudo-Taylor expansions and the Carathéodory-Fejér 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
Year2012
Volume386
Issue1
Pages308-318
ISSN (print)0022-247X
ISSN (electronic)1096-0813
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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.
PublisherAcademic Press
URLhttp://dx.doi.org/10.1016/j.jmaa.2011.08.001
DOI10.1016/j.jmaa.2011.08.001
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