2009/04/05 by Rachid Zarouf, Zarouf, Rachid
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · doi:10.48550/arxiv.0904.0775
openalex publication_date 2009/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite set σof the unit disc \mathbbD=\z∈ℂ:, | z|<1\ and a holomorphic function f in \mathbbD which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the norm ||g||Y among all functions g such that g|σ=f|σ. For Y=H∞, and for the corresponding interpolation constant c(σ, X, H∞), we show that c(σ, X, H∞)≤ aϕX(1-(1-r)/(n)) where n=#σ, r=maxλ∈σ|λ| and where ϕX(t) stands for the norm of the evaluation functional f↦ f(λ) on the space X. The upper bound is sharp over sets σwith given n and r.