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

Discretization of the orbit functions of G2

   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 SL- and SS-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 FM ⊂ F and added up with appropriate weight function.