2022/12/21 by John B. Conway, Liming Yang, Conway, John B. +1
Mathematics · #Analytic and geometric function theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2212.10811
openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1991, J. Thomson obtained a celebrated decomposition theorem for Pt(μ), the closed subspace of Lt(μ) spanned by the analytic polynomials, when 1 ≤ t < ı. In 2008, J. Brennan \citeb08 generalized Thomson's theorem to Rt(K, μ), the closed subspace of Lt(μ) spanned by the rational functions with poles off a compact subset K containing the support of μ, when the diameters of the components of \mathbb C∖ K are bounded below. We extend the above decomposition theorems for Rt(K, μ) when the boundary of K is not too wild.