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Liouville Theorem for Dunkl Polyharmonic Functions

Liouville Theorem for Dunkl Polyharmonic Functions

Assume that f is Dunkl polyharmonic in Rn (i.e. (Δh)p f = 0 for some integer p, where Δh 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 polynom...

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Main Authors: Ren, G., Liu, L.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148992
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spelling irk-123456789-1489922019-02-20T01:24:26Z Liouville Theorem for Dunkl Polyharmonic Functions Ren, G. Liu, L. Assume that f is Dunkl polyharmonic in Rn (i.e. (Δh)p f = 0 for some integer p, where Δh 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 function bounded above or below is constant. 2008 Article Liouville Theorem for Dunkl Polyharmonic Functions / G. Ren, L. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліор.: 17 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C52; 31A30; 35C10 http://dspace.nbuv.gov.ua/handle/123456789/148992 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Assume that f is Dunkl polyharmonic in Rn (i.e. (Δh)p f = 0 for some integer p, where Δh 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 function bounded above or below is constant.
format Article
author Ren, G.
Liu, L.
spellingShingle Ren, G.
Liu, L.
Liouville Theorem for Dunkl Polyharmonic Functions
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Ren, G.
Liu, L.
author_sort Ren, G.
title Liouville Theorem for Dunkl Polyharmonic Functions
title_short Liouville Theorem for Dunkl Polyharmonic Functions
title_full Liouville Theorem for Dunkl Polyharmonic Functions
title_fullStr Liouville Theorem for Dunkl Polyharmonic Functions
title_full_unstemmed Liouville Theorem for Dunkl Polyharmonic Functions
title_sort liouville theorem for dunkl polyharmonic functions
publisher Інститут математики НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/148992
citation_txt Liouville Theorem for Dunkl Polyharmonic Functions / G. Ren, L. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліор.: 17 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT reng liouvilletheoremfordunklpolyharmonicfunctions
AT liul liouvilletheoremfordunklpolyharmonicfunctions
first_indexed 2023-05-20T17:31:35Z
last_indexed 2023-05-20T17:31:35Z
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