The boundary analog of the Carathéodory-Schur interpolation problem

2010/08/19 by V. Bolotnikov, Vladimor Bolotnikov, Bolotnikov, Vladimor
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.1008.3364

arxiv created 2010/08/19 · openalex publication_date 2010/08/19 · arxiv updated 2010/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and sufficient conditions are given for the existence of a Schur-class function with the prescribed nontangential boundary expansion f(z)=s₀+s₁(z-t₀)+…+s_N(z-t₀)^N+o(|z-t₀|^N) at a given point t₀ on the unit circle.

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