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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Monic non-commutative orthogonal polynomials
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by Michael Anshelevich PDF
Proc. Amer. Math. Soc. 136 (2008), 2395-2405 Request permission

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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Additional 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