### Three dimensional C-, S- and E-transformsThree dimensional C-, S- and E-transforms

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 Author Nesterenko, M. ♦ Patera, J. Source arXiv.org Content type Text File Format PDF Date of Submission 2008-05-23 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword Mathematical Physics ♦ 42B99 ♦ 42C15 ♦ 58C40 ♦ math ♦ physics:math-ph Abstract 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 3-dimensional Euclidean space (continuous orthogonality), as well as when summed up over a lattice grid $F_M\subset F$ (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. Educational Use Research Learning Resource Type Article Page Count 24