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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148992 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Liouville Theorem for Dunkl Polyharmonic Functions / G. Ren, L. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліор.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609038269743104 |
|---|---|
| author | Ren, G. Liu, L. |
| author_facet | Ren, G. Liu, L. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-28T18:45:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148992 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T18:45:19Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ren, G. Liu, L. 2019-02-19T12:47:17Z 2019-02-19T12:47:17Z 2008 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 https://nasplib.isofts.kiev.ua/handle/123456789/148992 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. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The authors would like to thank the referees for their useful comments. The research is supported by the Unidade de Investiga¸c˜ao “Matem´atica e Aplica¸c˜oes” of University of Aveiro, and by the NNSF of China (No. 10771201), NCET-05-0539. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Liouville Theorem for Dunkl Polyharmonic Functions Article published earlier |
| spellingShingle | Liouville Theorem for Dunkl Polyharmonic Functions Ren, G. Liu, L. |
| title | 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_short | Liouville Theorem for Dunkl Polyharmonic Functions |
| title_sort | liouville theorem for dunkl polyharmonic functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148992 |
| work_keys_str_mv | AT reng liouvilletheoremfordunklpolyharmonicfunctions AT liul liouvilletheoremfordunklpolyharmonicfunctions |