Liouville Theorem for Dunkl Polyharmonic Functions

Symmetry, Integrability and Geometry: Methods and Applications

关键词: Liouville theorem;    Dunkl Laplacian;    polyharmonic functions;   

DOI  :  

来源: DOAJ

【 摘 要 】

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 $sge 2p-2$ is proved. As a direct corollary, a Dunkl harmonic function bounded above or below is constant.

【 授权许可】

Unknown