2008/05/23 by Maryna Nesterenko, M. Nesterenko, J. Patera
Computer Science · Mathematics · Physics and Astronomy · #Advanced Data Compression Techniques #Euclidean space #Fourier transform #Geometry #Image and Signal Denoising Methods #Lattice (music) #Lie group #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Orthogonality #Physics #Pure mathematics #math-ph #math.MP #msc:33-02 #msc:33E99 #msc:42B99 #msc:42C15 #msc:58C40
paper · pdf · doi:10.1088/1751-8113/41/47/475205
24 pages, 13 figures
arxiv created 2008/05/23 · openalex publication_date 2008/10/20 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
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 ( C -, S - and E -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 F of the three-dimensional Euclidean space (continuous orthogonality), as well as when summed up over a lattice grid F M ⊂ F (discrete orthogonality). The positive integer M sets up the density of the lattice containing F M . The expansion of functions given either on F or on F M is the paper's main focus.