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Dunkl OperatorIn 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 (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: -
for 1 <= i <= N, x ∈ RN, and f a smooth function on RN. Dunkl operators were first considered by mathematician Charles F. Dunkl.
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