An introduction to Dunkl theory and its analytic aspects

Understand

Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems.

• During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was closely connected with certain classes of special functions in one variable.
• During the eighties, several attempts were made, mainly by the Dutch school, to extend these results in higher rank (i.e.
• in several variables), until the discovery of Dunkl operators in the rational case and Cherednik operators in the trigonometric case.