Michael Anshelevich
Abstract
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. 1.
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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. 1.
Key concepts: Monic polynomial, Orthogonal polynomials, Mathematics, Recursion (computer science), Kravchuk polynomials, Discrete orthogonal polynomials, Pure mathematics, Algebra over a field