Asymptotic zero distribution for a class of multiple orthogonal polynomials

Coussement, E.; Coussement, J.; Van Assche, W.

doi:10.1090/S0002-9947-08-04535-2

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
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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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