The Dirichlet Problem for the Slab with Entire Data and a Difference Equation for Harmonic Functions

Canadian mathematical bulletin

Dmitry Khavinson²  Erik Lundberg¹  Hermann Render³ 

[1] Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA;Dept. of Mathematics and Statistics , University of South Florida, Tampa, FL, USA;School of Mathematics and Statistics, University College Dublin, Dublin, Ireland

关键词: reflection principle;    entire harmonic function;    analytic continuation;   

DOI  :  10.4153/CMB-2016-018-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

It is shown that the Dirichlet problem for the slab $(a,b) imesmathbb{R}^{d}$ with entire boundary data has an entire solution. The proofis basedon a generalized Schwarz reflection principle. Moreover, it isshown 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 $h$.

【 授权许可】

Unknown