Schur Parameters and the Carathéodory Class

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2 Citations (Scopus)

Abstract

The Schur (resp. Carathéodory) 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 Carathéodory function in terms of n independent variables γ1, ⋯ , γn. The mapping properties of those correspondences are also studied.

Original languageEnglish
Article number185
JournalResults in Mathematics
Volume74
Issue number4
DOIs
Publication statusPublished - 2019 Dec 1

Keywords

  • Schur algorithm
  • coefficient body
  • convex body
  • recursive formula

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

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