Dunkl Operators : Theory and Applications

  title={Dunkl Operators : Theory and Applications},
  author={Margit R{\"o}sler},
These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable particle systems of Calogero-MoserSutherland type, and discuss some systems of orthogonal polynomials associated with them. A major part is… CONTINUE READING