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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic zero distribution for a class of multiple orthogonal polynomials


Authors: E. Coussement, J. Coussement and W. Van Assche
Journal: Trans. Amer. Math. Soc. 360 (2008), 5571-5588
MSC (2000): Primary 33C45, 42C05; Secondary 15A18
Published electronically: May 20, 2008
MathSciNet review: 2415086
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Abstract: We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Piñeiro, Laguerre I and the example associated with modified Bessel functions. We also discuss an application to Toeplitz matrices.


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Additional Information

E. Coussement
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium

J. Coussement
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium

W. Van Assche
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
Email: walter@wis.kuleuven.be

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04535-2
PII: S 0002-9947(08)04535-2
Keywords: Multiple orthogonal polynomials, asymptotics
Received by editor(s): June 19, 2006
Received by editor(s) in revised form: January 31, 2007
Published electronically: May 20, 2008
Additional Notes: This work was supported by INTAS project 03-51-6637, by FWO projects G.0455.04 and G.0184.02 and by OT/04/21 of Katholieke Universiteit Leuven
The second author is a postdoctoral researcher at the Katholieke Universiteit Leuven (Belgium)
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.