Monic non-commutative orthogonal polynomials
arXiv:math/0702157 · doi:10.1090/S0002-9939-08-09306-4
Abstract
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.
10 pages