Title | ||
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Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials. |
Abstract | ||
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We investigate the ratio asymptotic behavior of the sequence (Qn)n=0∞ of multiple orthogonal polynomials associated with a Nikishin system of p≥1 measures that are compactly supported on the star-like set of p+1 rays S+={z∈C:zp+1≥0}. The main algebraic property of these polynomials is that they satisfy a three-term recurrence relation of the form zQn(z)=Qn+1(z)+anQn−p(z) with an>0 for all n≥p. Under a Rakhmanov-type condition on the measures generating the Nikishin system, we prove that the sequence of ratios Qn+1(z)∕Qn(z) and the sequence an of recurrence coefficients are limit periodic with period p(p+1). Our results complement some results obtained by the first author and Miña-Díaz in a recent paper in which algebraic properties and weak asymptotics of these polynomials were investigated. Our results also extend some results obtained by the first author in the case p=2. |
Year | DOI | Venue |
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2018 | 10.1016/j.jat.2017.10.002 | Journal of Approximation Theory |
Keywords | DocType | Volume |
primary,secondary | Journal | 225 |
ISSN | Citations | PageRank |
0021-9045 | 0 | 0.34 |
References | Authors | |
3 | 2 |
Name | Order | Citations | PageRank |
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Abey López García | 1 | 1 | 1.11 |
Guillermo López Lagomasino | 2 | 7 | 4.99 |