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Analyticity of a Nonlinear Operator Associated to the Conformal Representation in Schauder Spaces. An Integral Equation Approach

✍ Scribed by Massimo Lanza de Cristoforis; Sergei V. Rogosin

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 279 KB
Volume: 220
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200012)220:1<59::aid-mana59>3.0.co;2-7

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✦ Synopsis

We consider the Riemann map g ζ,w of the complex unit disk to the plane domain I[ζ] enclosed by the Jordan curve ζ and normalized by the conditions g ζ,w (0) = w, g ζ,w (0) > 0, where w is a point of I[ζ], and we present a nonlinear singular integral equation approach to prove that the nonlinear operator which takes the pair (ζ, w) to the map g (-1) ζ,w • ζ is real analytic in Schauder spaces.