Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Ming, Sugawa, Toshiyuki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2913650473