The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
|Title:||The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions||Authors:||Khavinson, Dmitry
|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|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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