Dunkl Operators Associated with Reflection Groups

Abstract

In this chapter we introduce the essential ingredient in the Dunkl theory of harmonic analysis. Since our purpose is to study harmonic analysis in weighted spaces, we start with the definition of a family of weight functions invariant under a reflection group in Section 2.1. Dunkl operators are a family of commuting first-order differential and difference operators associated with a reflection group, and are introduced in Section 2.2. The intertwining operator between the Dunkl operators and ordinary derivatives is discussed in Section 2.3.