Geodesic
The Reflection Principle for Banach Space-Valued Analytic Functions
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1189-1191

Voir la notice de l'article provenant de la source Cambridge University Press

We give sufficient conditions for the continuation of an analytic function with values in a Branch space. For analytic functions taking complex numbers as values, the principle is known as the Schwarz Reflection Principle.A function defined on a domain of the complex plane with values in a Banach space X is analytic if it possesses at each point Z 0 of the domain a convergent power series in z, with coefficients in X.THEOREM. Let D be a domain in the upper half-plane, and E a regular subset of the boundary of D. Suppose that E is an interval of the real axis (a,b). Let f be an analytic function defined on D, continuous up to E, taking values in a Banach space X. Let the image of D under f be Ω, and let Γ be the part of the boundary of Ω which is the image of E under f. 
Finkelstein, Mark. The Reflection Principle for Banach Space-Valued Analytic Functions. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1189-1191. doi: 10.4153/CJM-1969-131-0
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[1] 1. Dunford, N. and Schwartz, J. T., Linear operators. Part I: General theory (Interscience, New York, 1958). Google Scholar

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