Dunkl operator
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 a multiplicity function on R. 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. 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.
