2 research outputs found
Three dimensional C-, S- and E-transforms
Three dimensional continuous and discrete Fourier-like transforms, based on
the three simple and four semisimple compact Lie groups of rank 3, are
presented. For each simple Lie group, there are three families of special
functions (-, -, and -functions) on which the transforms are built.
Pertinent properties of the functions are described in detail, such as their
orthogonality within each family, when integrated over a finite region of
the 3-dimensional Euclidean space (continuous orthogonality), as well as when
summed up over a lattice grid (discrete orthogonality). The
positive integer sets up the density of the lattice containing . The
expansion of functions given either on or on is the paper's main
focus.Comment: 24 pages, 13 figure