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arXiv · 1902.02000

Schur parameters and Carathéodory class

Ming Li·Toshiyuki Sugawa
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Abstract

The Schur (resp. Carathéodory) class consists of all the analytic functions $f$ on the unit disk with $|f|\le 1$ (resp. $\Re f>0$ and $f(0)=1$). The Schur parameters $γ_0,γ_1,\dots (|γ_j|\le 1)$ are known to parametrize 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 $γ_1,\dots, γ_n$ with $|γ_j|\le 1.$ The mapping properties of those correspondences are also studied.

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Ming Li, Toshiyuki Sugawa. 2019-02-06. Schur parameters and Carathéodory class. https://arxiv.org/abs/1902.02000

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