A holomorphic map in infinite dimensions

Details A holomorphic map in infinite dimensions A holomorphic map in infinite dimensions

2006-09-22

arxiv.org/abs/math/0609632v4

Mathematics

Functional Analysis

7 pages, LaTeX; v2: a misprint corrected (p. 1, `x' added); v3(="v4"): " if we fix xi=xi^0, " added on p. 6

Scientific paper

We prove holomorphy E sqcap C(I,varPi) to C(I,varPi) of the map (x,y) mapsto x circ [id,y] where [id,y]:I owns t mapsto (t,y(t)) for a real compact interval I, and where varPi is a complex Banach space and E is a certain locally convex space of continuous functions x:I times varPi to varPi for which x(t,.) is holomorphic for all t in I. We also discuss application of this result to establishing a holomorphic solution map (xi,varphi) mapsto y for functions y:I to varPi satisfying the ordinary differential equation y' = varphi circ [id,y] with initial condition y(t_0) = xi .

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