Three dimensional C-, S- and E-transforms
| Autor: | Nesterenko, M., Patera, J. |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/41/47/475205 |
| Popis: | 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. Comment: 24 pages, 13 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|