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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


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