The Khavinson-Shapiro conjecture and polynomial decompositions
|Title:||The Khavinson-Shapiro conjecture and polynomial decompositions||Authors:||Lundberg, Erik
|Permanent link:||http://hdl.handle.net/10197/5490||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 polynomials; Fischer decompositions; Harmonic divisors; Algebraic 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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