Abstract
The Schur (resp. Carathéodory) class consists of all the analytic functions f on the unit disk with \(|f|\le 1\) (resp. \({\,{\text {Re}}\,}f>0\) and \(f(0)=1\)). The Schur parameters \(\gamma _0,\gamma _1,\dots (|\gamma _j|\le 1)\) 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 Carathéodory function in terms of n independent variables \(\gamma _1,\dots , \gamma _n\). The mapping properties of those correspondences are also studied.
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Acknowledgements
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.
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Li, M., Sugawa, T. Schur Parameters and the Carathéodory Class. Results Math 74, 185 (2019). https://doi.org/10.1007/s00025-019-1107-7
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DOI: https://doi.org/10.1007/s00025-019-1107-7