Monic non-commutative orthogonal polynomials
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- by Michael Anshelevich
- Proc. Amer. Math. Soc. 136 (2008), 2395-2405
- DOI: https://doi.org/10.1090/S0002-9939-08-09306-4
- Published electronically: February 20, 2008
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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.References
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Bibliographic Information
- Michael Anshelevich
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- Email: manshel@math.tamu.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2395-2405
- MSC (2000): Primary 05E35; Secondary 46Nxx
- DOI: https://doi.org/10.1090/S0002-9939-08-09306-4
- MathSciNet review: 2390506