Dunkl operator (original) (raw)
In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space. Formally, let G be a Coxeter group with reduced root system R and kv an arbitrary "multiplicity" function on R (so ku = kv whenever the reflections σu and σv corresponding to the roots u and v are conjugate in G). Then, the Dunkl operator is defined by: where is the i-th component of v, 1 ≤ i ≤ N, x in RN, and f a smooth function on RN.
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space. Formally, let G be a Coxeter group with reduced root system R and kv an arbitrary "multiplicity" function on R (so ku = kv whenever the reflections σu and σv corresponding to the roots u and v are conjugate in G). Then, the Dunkl operator is defined by: where is the i-th component of v, 1 ≤ i ≤ N, x in RN, and f a smooth function on RN. Dunkl operators were introduced by Charles Dunkl. One of Dunkl's major results was that Dunkl operators "commute," that is, they satisfy just as partial derivatives do. Thus Dunkl operators represent a meaningful generalization of partial derivatives. (en) |
| dbo:wikiPageID | 947234 (xsd:integer) |
| dbo:wikiPageLength | 1643 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 988724316 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Mathematics dbr:Lie_groups dbc:Lie_groups dbr:Differential_operator dbr:Reflection_(mathematics) dbr:Coxeter_group dbr:Transactions_of_the_American_Mathematical_Society dbr:Mathematical_operator |
| dbp:authorlink | Charles F. Dunkl (en) |
| dbp:first | Charles (en) |
| dbp:last | Dunkl (en) |
| dbp:wikiPageUsesTemplate | dbt:Citation dbt:Harvs |
| dbp:year | 1989 (xsd:integer) |
| dcterms:subject | dbc:Lie_groups |
| rdf:type | yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264 |
| rdfs:comment | In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space. Formally, let G be a Coxeter group with reduced root system R and kv an arbitrary "multiplicity" function on R (so ku = kv whenever the reflections σu and σv corresponding to the roots u and v are conjugate in G). Then, the Dunkl operator is defined by: where is the i-th component of v, 1 ≤ i ≤ N, x in RN, and f a smooth function on RN. (en) |
| rdfs:label | Dunkl operator (en) |
| owl:sameAs | freebase:Dunkl operator wikidata:Dunkl operator https://global.dbpedia.org/id/4jCGE yago-res:Dunkl operator |
| prov:wasDerivedFrom | wikipedia-en:Dunkl_operator?oldid=988724316&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Dunkl_operator |
| is dbo:wikiPageRedirects of | dbr:Dunkl-Cherednik_operator dbr:Dunkl–Cherednik_operator dbr:Jacobi-Dunkl_operator dbr:Jacobi–Dunkl_operator |
| is dbo:wikiPageWikiLink of | dbr:Charles_F._Dunkl dbr:Eric_M._Opdam dbr:Dunkl-Cherednik_operator dbr:List_of_Lie_groups_topics dbr:Margit_Rösler dbr:List_of_special_functions_and_eponyms dbr:Dunkl–Cherednik_operator dbr:Jacobi-Dunkl_operator dbr:Jacobi–Dunkl_operator |
| is foaf:primaryTopic of | wikipedia-en:Dunkl_operator |