%0 Journal Article
%T Holomorphic Continuation via Laplace-Fourier series
%A O. Kounchev
%A H. Render
%J Mathematics
%D 2011
%I arXiv
%X Let $B_{R}$ be the ball in the euclidean space $\mathbb{R}^{n}$ with center 0 and radius $R$ and let $f$ be a complex-valued, infinitely differentiable function on $B_{R}.$ We show that the Laplace-Fourier series of $f$ has a holomorphic extension which converges compactly in the Lie ball $\hat {B_{R}}$ in the complex space $\mathbb{C}^{n}$ when one assumes a natural estimate for the Laplace-Fourier coefficients.
%U http://arxiv.org/abs/1111.2699v1