Abstract
Given a functionρ: Ω→ℝ+ on a domain Ω spread over an infinite dimensional complex Banach space E with a Schauder basis such that -logρ is plurisubharmonic and ρ≦dΩ (dΩ denotes the boundary distance on Ω) one can find a holomorphic function f: Ω→ℂ withρ f≦ρ, whereρ f is the radius of convergence of f. If, in addition,ρ is locally Lipschitz continuous with constant 1, f can be chosen so that (3M)−1 ρ≦ρ f≦ρ, where M is the basis constant of E. In the particular case of E=ℓ 1 there are holomorphic functions f on Ω withρ=ρ f.
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Schottenloher, M. Holomorphe Funktionen auf Gebieten über Banach-Räumen zu vorgegebenen Konvergenzradien. Manuscripta Math 21, 315–327 (1977). https://doi.org/10.1007/BF01167851
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DOI: https://doi.org/10.1007/BF01167851