Geodesic
Liouville Theorem for Dunkl Polyharmonic Functions
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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Assume that $f$ is Dunkl polyharmonic in $\mathbb R^n$ (i.e. $(\Delta_h)^p f=0$ for some integer $p$, where $\Delta_h$ is the Dunkl Laplacian associated to a root system $R$ and to a multiplicity function $\kappa$, 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.
Keywords: Liouville theorem; Dunkl Laplacian; polyharmonic functions. 
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     author = {Guangbin Ren and Liang Liu},
     title = {Liouville {Theorem} for {Dunkl} {Polyharmonic} {Functions}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a75/}
}
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Guangbin Ren; Liang Liu. Liouville Theorem for Dunkl Polyharmonic Functions. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a75/

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