Marzena Szajewska (Institute of Mathematics, University of Bialystok, Poland)

Discretization of the orbit functions of G₂

Abstract:
   In this talk, we consider four infinite families of special functions of two real variables, based on the compact simple Lie group G₂. Two of the four families (called C- and S-functions) are well known. Two new families of G₂-functions are denoted as S^L- and S^S-functions. They are orthogonal when integrated over a finite region F of the Euclidean space. They are also orthogonal as discrete functions when their values are sampled at the lattice points F^M ⊂ F and added up with appropriate weight function.