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Noncommutative Biorthogonal Polynomials (1009.5472v2)
Published 28 Sep 2010 in math.QA, math-ph, math.MP, and math.RA
Abstract: The idea of orthogonal polynomials has been generalized in two ways to achieve new types of polynomials: noncommutative orthogonal polynomials and biorthogonal polynomials. This paper brings these two different generalizations together to present a completely algebraic definition of noncommutative biorthogonal polynomials. It then goes on to obtain recurrence relations for some types of biorthogonal polynomials and concludes with a broad extension of Favard's theorem.