A Characterization of the Khavinson-Shapiro Conjecture Via Fischer Operators

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Title: A Characterization of the Khavinson-Shapiro Conjecture Via Fischer Operators
Authors: Render, Hermann
Permanent link: http://hdl.handle.net/10197/9584
Date: Oct-2016
Online since: 2019-01-07T14:04:27Z
Abstract: The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that property (KS) for a domain Ω is equivalent to the surjectivity of a Fischer operator associated to the domain Ω.
Type of material: Journal Article
Publisher: Springer
Journal: Potential Analysis
Volume: 45
Issue: 3
Start page: 539
End page: 543
Copyright (published version): 2017 Springer
Keywords: Dirichlet problemHarmonic extensionKhavinson-Shapiro conjecture
DOI: 10.1007/s11118-016-9555-0
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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