Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Monic non-commutative orthogonal polynomials

Author: Michael Anshelevich
Journal: Proc. Amer. Math. Soc. 136 (2008), 2395-2405
MSC (2000): Primary 05E35; Secondary 46Nxx
Published electronically: February 20, 2008
MathSciNet review: 2390506
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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.

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Michael Anshelevich
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368

Received by editor(s): February 8, 2007
Received by editor(s) in revised form: June 19, 2007
Published electronically: February 20, 2008
Additional Notes: This work was supported in part by NSF grant DMS-0613195
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.