Liouville Theorem for Dunkl Polyharmonic Functions
نویسندگان
چکیده
منابع مشابه
Liouville Theorem for Dunkl Polyharmonic Functions
Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆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 ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl transform
Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
متن کاملTitchmarsh theorem for Jacobi Dini-Lipshitz functions
Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...
متن کاملIntegration of polyharmonic functions
The results in this paper are motivated by two analogies. First, m-harmonic functions in Rn are extensions of the univariate algebraic polynomials of odd degree 2m−1. Second, Gauss’ and Pizzetti’s mean value formulae are natural multivariate analogues of the rectangular and Taylor’s quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules cou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2008
ISSN: 1815-0659
DOI: 10.3842/sigma.2008.076