Orthogonal polynomials associated with the Dirac operator in Euclidean space
This paper deals with a method of generalizing the theory of classical orthogonal polynomials to the higher dimensional cases. The second order differential operator of these polynomials is split into the derivation operator, considered as an operator between Hilbert spaces and its adjoint. In the case of higher dimensions the derivation operator is replaced by the Dirac operator. Jacobi polynomials, thereby Gegenbauer, Chebyshev and Legendre polynomials, Laguerre and Hermite polynomials are generalized to higher dimensions.
scientific article; zbMATH DE number 60826