Nikishin Systems Are Perfect
Nikishin Systems Are Perfect
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DOI：
10.1007/s00365-011-9139-6
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发表时间：
2010-01
影响因子：
2.7
通讯作者：
U. F. Prieto;G. Lagomasino
中科院分区：
文献类型：
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作者：
U. F. Prieto;G. Lagomasino
K. Mahler 在他为解析函数的联立 Hermite-Padé 近似开发的一般理论中引入了完美系统的概念。我们证明 Nikishin 系统是完美的，提供了迄今为止这一重要属性所拥有的最大类功能系统。因此，在 Nikishin 系统的背景下，我们得到：马尔可夫定理对联立 Hermite-Padé 近似的推广、高斯-雅可比型联立求积规则收敛的一般结果、多重正交多项式一般序列的对数渐近、以及混合型多重正交的比率渐近的 Denisov-Rakhmanov 定理的推广多项式。
K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite–Padé approximation of analytic functions. We prove that Nikishin systems are perfect, providing by far the largest class of systems of functions for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov’s theorem to simultaneous Hermite–Padé approximation, a general result on the convergence of simultaneous quadrature rules of Gauss–Jacobi type, the logarithmic asymptotics of general sequences of multiple orthogonal polynomials, and an extension of the Denisov–Rakhmanov theorem for the ratio asymptotics of mixed type multiple orthogonal polynomials.