Asymptotic zero distribution for a class of multiple orthogonal polynomials
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- 20 May 2008
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 360 (10) , 5571-5588
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.Keywords
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This publication has 21 references indexed in Scilit:
- On the limit behavior of recurrence coefficients for multiple orthogonal polynomialsJournal of Approximation Theory, 2006
- Generalizations of orthogonal polynomialsJournal of Computational and Applied Mathematics, 2005
- Large n Limit of Gaussian Random Matrices with External Source, Part IICommunications in Mathematical Physics, 2005
- Large n Limit of Gaussian Random Matrices with External Source, Part ICommunications in Mathematical Physics, 2004
- Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence CoefficientsJournal of Approximation Theory, 2001
- The Genetic Sums' Representation for the Moments of a System of Stieltjes Functions and its ApplicationConstructive Approximation, 2000
- The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence CoefficientsJournal of Approximation Theory, 1999
- Logarithmic Potentials with External Fields1997
- Chebyshev quadrature for measures with a strong singularityJournal of Computational and Applied Mathematics, 1995
- Simultaneous pade approximation and orthogonality1985