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Marzena Szajewska (Institute of Mathematics, University of Bialystok, Poland)
Discretization of the orbit functions of G_{2}
Abstract:
In this talk, we consider four infinite families of special functions of two real variables,
based on the compact simple Lie group G_{2}. Two of the four families (called C and Sfunctions) are well known.
Two new families of G_{2}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.
