Holomorphic Continuation via Laplace-Fourier series

Abstract

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 $\widehat{B_R}$ in the complex space ${\mathbb{C}}^n$ when one assumes a natural estimate for the Laplace-Fourier coefficients.

10 pages, almost the same version appeared in Proc. Conference on Complex analysis and dynamical systems III, Contemporary Mathematics, 2008

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