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 | References | Similar Articles | Additional Information

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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Additional Information

**Michael Anshelevich**

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

Email:
manshel@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09306-4

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.