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Monic non-commutative orthogonal polynomials
Author(s):
Michael
Anshelevich
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2395-2405.
MSC (2000):
Primary 05E35;
Secondary 46Nxx
Posted:
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:
-
- [Ans06]
- Michael Anshelevich, Orthogonal polynomials with a resolvent-type generating function, math.CO/0410482, accepted for publication by Transactions of the AMS, 2006.
- [Ans07]
- -, Free Meixner states, math.CO/0702158, accepted for publication by Communications in Mathematical Physics, 2007.
- [BC04]
- T. Banks and T. Constantinescu, Orthogonal polynomials in several non-commuting variables. II, math.FA/0412528, 2004.
- [BCJ05]
- T. Banks, T. Constantinescu, and J. L. Johnson, Relations on non-commutative variables and associated orthogonal polynomials, Operator theory, systems theory and scattering theory: multidimensional generalizations, Oper. Theory Adv. Appl., vol. 157, Birkhäuser, Basel, 2005, pp. 61-90. MR 2129643 (2006d:47012)
- [DES]
- Ioana Dumitriu, Alan Edelman, and Gene Shuman, MOPS: Multivariate orthogonal polynomials (symbolically), J. Symbolic Comput. 42 (2007), 587-620. MR 2325917
- [DX01]
- Charles F. Dunkl and Yuan Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and its Applications, vol. 81, Cambridge University Press, Cambridge, 2001. MR 2002m:33001
- [Fla80]
- P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980), no. 2, 125-161. MR 82f:05002a
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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:
10.1090/S0002-9939-08-09306-4
PII:
S 0002-9939(08)09306-4
Received by editor(s):
February 8, 2007,
Received by editor(s) in revised form:
June 19, 2007
Posted:
February 20, 2008
Additional Notes:
This work was supported in part by NSF grant DMS-0613195
Communicated by:
Jim Haglund
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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