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
DOI:
https://doi.org/10.1090/S0002-9947-08-04535-2
Published electronically:
May 20, 2008
MathSciNet review:
2415086
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 200Â B, 3001 Leuven, Belgium
J. Coussement
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200Â B, 3001 Leuven, Belgium
W. Van Assche
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200Â B, 3001 Leuven, Belgium
MR Author ID:
176825
ORCID:
0000-0003-3446-6936
Email:
walter@wis.kuleuven.be
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.