location:  Publications → journals → CMB
Abstract view

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

Published:2016-04-19
Printed: Mar 2017
• Dmitry Khavinson,
Dept. of Mathematics and Statistics , University of South Florida, Tampa, FL, USA
• Erik Lundberg,
Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA
• Hermann Render,
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland
 Format: LaTeX MathJax PDF

## 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 $h ( t+1,y) -h (t,y) =g ( t,y)$ has an entire harmonic solution $h$.
 Keywords: reflection principle, entire harmonic function, analytic continuation
 MSC Classifications: 31B20 - Boundary value and inverse problems 31B05 - Harmonic, subharmonic, superharmonic functions

 top of page | contact us | privacy | site map |