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A lower bound on the radius of analyticity of a power series in a real Banach space

Timothy Nguyen — 2009

Studia Mathematica

Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.

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