Orthogonal polynomials in several variables. I
classification
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polynomialsorthogonalintroduceseveralvariableschristoffel-darbouxclassesdiscuss
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In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations for these polynomials, Christoffel-Darboux formulas, and Jacobi type matrices.
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