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The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
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| Download | 2016KLRPaper2.pdf | 116.14 kB | Adobe PDF |
| 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 | Online since: | 2018-11-30T16:37:37Z | 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 principle; Entire harmonic function; Analytic continuation | DOI: | 10.4153/CMB-2016-018-x | Language: | en | Status of Item: | Peer reviewed | This item is made available under a Creative Commons License: | https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ |
| Appears in Collections: | Mathematics and Statistics Research Collection |
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