Abstract
Weak-star asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e., the zeros of their determinants) on ℝ from two different assumptions: first from the convergence of matrix coefficients occurring in the three-term recurrence for these polynomials; and, second, from conditions on the generating matrix measure. The matrix analogues of the Chebyshev polynomials of the first kind are also investigated.
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The research of the first and second authors has been supported by DGICYT ref. PB96-1321-C02-01, and the research of the third author was supported, in part, by the U.S. National Science Foundation under the grant DMS-9501130.
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Duran, A.J., Lopez-Rodriguez, P. & Saff, E.B. Zero asymptotic behaviour for orthogonal matrix polynomials. J. Anal. Math. 78, 37–60 (1999). https://doi.org/10.1007/BF02791128
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DOI: https://doi.org/10.1007/BF02791128