Geodesic
The Dirichlet Problem for the Slab with Entire Data and a Difference Equation for Harmonic Functions
Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 146-153

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It is shown that the Dirichlet problem for the slab $\left( a,\,b \right)\,\times \,{{\mathbb{R}}^{d}}$ 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 $h$ .
DOI : 10.4153/CMB-2016-018-x
Mots-clés : 31B20, 31B05, reflection principle, entire harmonic function, analytic continuation 
Khavinson, Dmitry; Lundberg, Erik; Render, Hermann. The Dirichlet Problem for the Slab with Entire Data and a Difference Equation for Harmonic Functions. Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 146-153. doi: 10.4153/CMB-2016-018-x
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     title = {The {Dirichlet} {Problem} for the {Slab} with {Entire} {Data} and a {Difference} {Equation} for {Harmonic} {Functions}},
     journal = {Canadian mathematical bulletin},
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