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

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Title: The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
Authors: Khavinson, Dmitry
Lundberg, Erik
Render, Hermann
Permanent link: http://hdl.handle.net/10197/9575
Date: Mar-2017
Abstract: It is shown that the Dirichlet problem for the slab (a,b)×Rd 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.
Type of material: Journal Article
Publisher: Canadian Mathematical Society
Journal: Canadian Mathematics Bulletin
Volume: 60
Start page: 146
End page: 153
Copyright (published version): 2016 Canadian Mathematical Society
Keywords: Reflection principleEntire harmonic functionAnalytic continuation
DOI: 10.4153/CMB-2016-018-x
Language: en
Status of Item: Peer reviewed
metadata.dc.date.available: 2018-11-30T16:37:37Z
Appears in Collections:Mathematics and Statistics Research Collection

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