Liouville Theorem for Dunkl Polyharmonic Functions

dc.creatorRen, Guangbin
dc.creatorLiu, Liang
dc.date2008-11-06
dc.date.accessioned2026-07-07T10:16:25Z
dc.date.available2026-07-07T10:16:25Z
dc.descriptionAssume that $f$ is Dunkl polyharmonic in $\mathbb{R}^n$ (i.e. $(Δ_h)^p f=0$ for some integer $p$, where $Δ_h$ is the Dunkl Laplacian associated to a root system $R$ and to a multiplicity function $κ$, defined on $R$ and invariant with respect to the finite Coxeter group). Necessary and successful condition that $f$ is a polynomial of degree $\le s$ for $s\ge 2p-2$ is proved. As a direct corollary, a Dunkl harmonic function bounded above or below is constant.
dc.descriptionThis is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0811.0962
dc.identifierhttp://arxiv.org/abs/0811.0962
dc.identifierSIGMA 4 (2008), 076, 6 pages
dc.identifierdoi:10.3842/SIGMA.2008.076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173499
dc.subjectClassical Analysis and ODEs
dc.subjectAnalysis of PDEs
dc.titleLiouville Theorem for Dunkl Polyharmonic Functions
dc.typetext

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