两个Nikishin系统的混合型多重正交多项式
Mixed type multiple orthogonal polynomials for two Nikishin systems
摘要：
研究了由一个Nikishin系统构造的满足正交条件的线性型关于由另一个Nikishin系统生成的测度系统的对数渐近性和比渐近性.该构造结合了I型和II型多个正交多项式。该线性型的对数渐近性用对数势的一个相关向量值平衡问题的极值解表示。比率渐近是通过一个适当的黎曼曲面的保角表示亏格为零的扩充复平面上。
英文摘要：
We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an associated vector valued equilibrium problem for the logarithmic potential. The ratio asymptotic is described by means of a conformal representation of an appropriate Riemann surface of genus zero onto the extended complex plane.
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