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arXiv · 1602.01823

The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions

Dmitry Khavinson·Erik Lundberg·Hermann Render
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Abstract

It is shown that the Dirichlet problem for the slab $(a,b) \times \mathbb{R}^{d}$ with entire boundary data has an entire solution. The proof is based on a generalized Schwarz reflection principle. Moreover, it is shown that for a given entire harmonic function $g$ the inhomogeneous difference equation $h\left( t+1,y\right) -h\left(t,y\right) =g\left(t,y\right)$ has an entire harmonic solution $h$.

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Dmitry Khavinson, Erik Lundberg, Hermann Render. 2016-02-04. The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions. https://arxiv.org/abs/1602.01823

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