Monic non-commutative orthogonal polynomials
classification
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polynomialsmonicnon-commutativeorthogonalalgebracharacterizationscharacterizedeterminants
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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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