The Khavinson-Shapiro conjecture and polynomial decompositions

DC FieldValueLanguage
dc.contributor.authorLundberg, Erik-
dc.contributor.authorRender, Hermann-
dc.date.accessioned2014-03-27T15:51:19Z-
dc.date.available2014-03-27T15:51:19Z-
dc.date.copyright2011 Elsevieren
dc.date.issued2011-04-15-
dc.identifier.citationJournal of Mathematical Analysis and Applicationsen
dc.identifier.urihttp://hdl.handle.net/10197/5490-
dc.description.abstractThe 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.en
dc.language.isoenen
dc.publisherElsevieren
dc.rightsThis is the author.s version of a work that was accepted for publication in J. Math. Analysis Appl. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in E. Lundberg, H. Render : The Khavinson-Shapiro Conjecture and Polynomial Decompositions. J. Math. Analysis Appl., 376 2011, pp.506-513. DOI:10.1016/j.jmaa.2010.09.069en
dc.subjectHarmonic and polyharmonic polynomialsen
dc.subjectFischer decompositionsen
dc.subjectHarmonic divisorsen
dc.subjectAlgebraic Dirichlet problemsen
dc.titleThe Khavinson-Shapiro conjecture and polynomial decompositionsen
dc.typeJournal Articleen
dc.internal.authorcontactotherhermann.render@ucd.ie-
dc.internal.availabilityFull text availableen
dc.statusPeer revieweden
dc.identifier.volume376en
dc.identifier.issue2en
dc.identifier.startpage506en
dc.identifier.endpage513en
dc.identifier.doi10.1016/j.jmaa.2010.09.069-
dc.neeo.contributorLundberg|Erik|aut|-
dc.neeo.contributorRender|Hermann|aut|-
dc.description.adminAD 26/03/2014en
dc.internal.rmsid202064895-
dc.date.updated2014-03-01T10:21:23Z-
item.grantfulltextopen-
item.fulltextWith Fulltext-
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