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Statements

Subject Item
dbr:Charles_F._Dunkl
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dbr:Dunkl_operator
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dbr:Dunkl_operator
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yago:Abstraction100002137 yago:WikicatLieGroups yago:Group100031264
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Dunkl operator
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.
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947234
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988724316
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dbr:Transactions_of_the_American_Mathematical_Society dbr:Reflection_(mathematics) dbr:Mathematics dbc:Lie_groups dbr:Coxeter_group dbr:Differential_operator dbr:Lie_groups dbr:Mathematical_operator
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Charles F. Dunkl
dbp:first
Charles
dbp:last
Dunkl
dbp:year
1989
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.
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wikipedia-en:Dunkl_operator?oldid=988724316&ns=0
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