1. CMB Online first
 Khavinson, Dmitry; Lundberg, Erik; Render, Hermann

The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
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 $h
( t+1,y) h (t,y) =g ( t,y)$
has an entire harmonic solution $h$.
Keywords:reflection principle, entire harmonic function, analytic continuation Categories:31B20, 31B05 

2. CMB 2003 (vol 46 pp. 252)
3. CMB 1997 (vol 40 pp. 60)
 Khavinson, Dmitry

Cauchy's problem for harmonic functions with entire data on a sphere
We give an elementary potentialtheoretic proof of a theorem of
G.~Johnsson: all solutions of Cauchy's problems for the Laplace
equations with an entire data on a sphere extend harmonically to
the whole space ${\bf R}^N$ except, perhaps, for the center of the
sphere.
Keywords:harmonic functions, Cauchy's problem, homogeneous harmonics Categories:35B60, 31B20 
