We consider an exceptional simple Lie group G and a positive integer M and introduce a certain finite set of lattice points FM. The group G and the corresponding affine Weyl group induce the symmetry of FM, the number M determines the density of the grid FM. We present a construction of the set FM and explicitly count the numbers of its points |FM| for the cases of G2 and F4. We specify the maximal sets of pairwise orthogonal C—and S—functions over FM. These finite sets allow us to calculate Fourier like discrete expansions of arbitrary discrete functions on FM. Application of these discrete transforms to interpolation is presented on the group F4.

This content is only available via PDF.
You do not currently have access to this content.