@article{7e1b5732d1e348a397721efdc9810e96,
title = "Schur Parameters and the Carath{\'e}odory Class",
abstract = "The Schur (resp. Carath{\'e}odory) class consists of all the analytic functions f on the unit disk with | f| ≤ 1 (resp. Ref>0 and f(0) = 1). The Schur parameters γ, γ1, ⋯ (| γj| ≤ 1) are known to parameterize the coefficients of functions in the Schur class. By employing a recursive formula for it, we describe the n-th coefficient of a Carath{\'e}odory function in terms of n independent variables γ1, ⋯ , γn. The mapping properties of those correspondences are also studied.",
keywords = "Schur algorithm, coefficient body, convex body, recursive formula",
author = "Ming Li and Toshiyuki Sugawa",
note = "Funding Information: The authors would like to express their sincere thanks to the referees for careful checkings and helpful comments. The research is financially supported in part by Hunan Provincial Key Laboratory of Mathematical Modelling and Analysis in Engineering (Changsha University of Science & Technology) and JSPS KAKENHI Grant Number JP17H02847. Funding Information: The authors would like to express their sincere thanks to the referees for careful checkings and helpful comments. The research is financially supported in part by Hunan Provincial Key Laboratory of Mathematical Modelling and Analysis in Engineering (Changsha University of Science & Technology) and JSPS KAKENHI Grant Number JP17H02847. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s00025-019-1107-7",
language = "English",
volume = "74",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Birkhauser Verlag Basel",
number = "4",
}