Introduction: Spherical Harmonics and Fourier Transform

Abstract

The purpose of these lecture notes is to provide an introduction to two related topics: h-harmonics and the Dunkl transform. These are extensions of the classical spherical harmonics and the Fourier transform, in which the underlying rotation group is replaced by a finite reflection group. This chapter serves as an introduction, in which we briefly recall classical results on the spherical harmonics and the Fourier transform. Since all results are classical, no proof will be given.