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Pseudo-Taylor expansions and the Carathéodory-Fejér problem

Lookup NU author(s): Professor Jim Agler, Dr Zinaida LykovaORCiD, Professor Nicholas Young



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.

Publication metadata

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

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Analysis and Applications

Year: 2012

Volume: 386

Issue: 1

Pages: 308-318

Print publication date: 06/08/2011

Date deposited: 08/01/2011

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

Publisher: Academic Press


DOI: 10.1016/j.jmaa.2011.08.001


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Funder referenceFunder name
4918London Mathematical Society
DMS 0801259National Science Foundation