Radius of analyticity of a power series on real Banach spaces

摘要

If F(x) is a power series, rho its radius of uniform convergence and rho(A) its radius of analyticity, we improve T. Nguyen's result to rho(A) >= rho/root 2 and give some respective results for the nth Frechet derivative of F(x). (C) 2015 Elsevier Inc. All rights reserved.