Holomorphic Continuation via Laplace-Fourier series

Details Holomorphic Continuation via Laplace-Fourier series Holomorphic Continuation via Laplace-Fourier series

2011-11-11

arxiv.org/abs/1111.2699v1

Contemporary Mathematics 2008; Volume: 455

Mathematics

Functional Analysis

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

Scientific paper

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.

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