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297:{\displaystyle T_{i}f(x)={\frac {\partial }{\partial x_{i}}}f(x)+\sum _{v\in R_{+}}k_{v}{\frac {f(x)-f(x\sigma _{v})}{\left\langle x,v\right\rangle }}v_{i}}
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just as partial derivatives do. Thus Dunkl operators represent a meaningful generalization of partial derivatives.
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Dunkl, Charles F. (1989), "Differential-difference operators associated to reflection groups",
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377:). One of Dunkl's major results was that Dunkl operators "commute," that is, they satisfy
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486:Transactions of the American Mathematical Society
466:{\displaystyle T_{i}(T_{j}f(x))=T_{j}(T_{i}f(x))}
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67:an arbitrary "multiplicity" function on
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369:Dunkl operators were introduced by
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23:, particularly the study of
101:corresponding to the roots
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89:whenever the reflections σ
54:with reduced root system
43:in an underlying space.
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37:differential operators
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362:a smooth function on
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327:{\displaystyle v_{i}}
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33:mathematical operator
31:is a certain kind of
16:Mathematical operator
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371:Charles Dunkl
338:-th component of
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109:are conjugate in
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493:(1): 167–183,
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115:Dunkl operator
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46:Formally, let
29:Dunkl operator
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35:, involving
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41:reflections
21:mathematics
533:Lie groups
477:References
25:Lie groups
509:0002-9947
251:σ
238:−
198:∈
191:∑
159:∂
155:∂
39:but also
527:Category
279:⟩
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307:where
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505:ISSN
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