T-universal Functions With Prescribed Approximation Curves

2003/11/13 by Daniel Mayenberger, Mayenberger, Daniel
Mathematics · #32E30 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32E30

paper · pdf · doi:10.48550/arxiv.math/0311229

References corrected

arxiv created 2003/11/13 · openalex publication_date 2003/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let be F a family of curves in the unit disc. We show that the set of all functions f holomorphic on the unit disc, which satisfy the following condition, is G-delta and dense in the space of all functions holomorphic on the unit disc: For each compact set K with connected complement, each function g continuous on K and holomorphic on its interior, every point t on the unit circle, every curve C in F (ending in t) and any e>0 there exist numbers 0

Related

• Universal Radial Approximation in Spaces of Analytic Functions
• Abel universal functions: boundary behaviour and Taylor polynomials
• On universality and convergence of the Fourier series of functions in the disc algebra
• Universal Taylor series, conformal mappings and boundary behaviour
• Universal Taylor Series On Convex Subsets Of \MathbbC^N