Relative asymptotic of multiple orthogonal polynomials for Nikishin systems |
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Authors: | Abey Lpez García Guillermo Lpez Lagomasino |
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Institution: | aDpto. de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad 15, 28911 Leganés, Madrid, Spain |
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Abstract: | We prove the relative asymptotic behavior for the ratio of two sequences of multiple orthogonal polynomials with respect to the Nikishin systems of measures. The first Nikishin system is such that for each k, σk has a constant sign on its compact support consisting of an interval , on which almost everywhere, and a discrete set without accumulation points in . If denotes the smallest interval containing , we assume that Δk∩Δk+1=0/, k=1,…,m−1. The second Nikishin system is a perturbation of the first by means of rational functions rk, k=1,…,m, whose zeros and poles lie in . |
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Keywords: | Multiple orthogonal polynomials Nikishin systems Relative asymptotic |
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