The Khavinson-Shapiro conjecture and polynomial decompositions

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Title: The Khavinson-Shapiro conjecture and polynomial decompositions
Authors: Lundberg, Erik
Render, Hermann
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Date: 15-Apr-2011
Online since: 2014-03-27T15:51:19Z
Abstract: The main result of the paper states the following: Let ψ be a polynomial in n variables of degree t: Suppose that there exists a constant C > 0 such that any polynomial f has a polynomial decomposition f = ψ qf + hf with khf = 0 and deg qf deg f + C: Then deg ψ 2k. Here ∆k is the kth iterate of the Laplace operator ∆ : As an application, new classes of domains in Rn are identi ed for which the Khavinson-Shapiro conjecture holds.
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Mathematical Analysis and Applications
Volume: 376
Issue: 2
Start page: 506
End page: 513
Copyright (published version): 2011 Elsevier
Keywords: Harmonic and polyharmonic polynomialsFischer decompositionsHarmonic divisorsAlgebraic Dirichlet problems
DOI: 10.1016/j.jmaa.2010.09.069
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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