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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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148992 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Liouville Theorem for Dunkl Polyharmonic Functions / G. Ren, L. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліор.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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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 |
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AT reng liouvilletheoremfordunklpolyharmonicfunctions AT liul liouvilletheoremfordunklpolyharmonicfunctions |
| first_indexed |
2023-05-20T17:31:35Z |
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2023-05-20T17:31:35Z |
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1796153498603094016 |