Browse by author
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.
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
URL: http://dx.doi.org/10.1016/j.jmaa.2011.08.001
DOI: 10.1016/j.jmaa.2011.08.001
Altmetrics provided by Altmetric