Monic non-commutative orthogonal polynomials

Details Monic non-commutative orthogonal polynomials Monic non-commutative orthogonal polynomials

2007-02-06

arxiv.org/abs/math/0702157v1

Proc. Amer. Math. Soc. 136 (2008), 2395-2405

Mathematics

Combinatorics

10 pages

Scientific paper

10.1090/S0002-9939-08-09306-4

Among all states on the algebra of non-commutative polynomials, we
characterize the ones that have monic orthogonal polynomials. The
characterizations involve recursion relations, Hankel-type determinants, and a
representation as a joint distribution of operators on a Fock space.

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