Nikishin systems are perfect. The case of unbounded and touching supports

作者：Fidalgo Prieto U; Lopez Lagomasino G

来源：Journal of Approximation Theory, 2011, 163(6): 779-811.

DOI：10.1016/j.jat.2011.03.004

• Perfect systems
• Nikishin systems
• Multiple orthogonal polynomials
• Mixed type orthogonal polynomials
• Bi-orthogonal polynomials
• Stieltjes theorem

K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Pade approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and non-intersecting consecutive supports contained on the real line, are perfect. Here, we prove that they are also perfect when the supports of the generating measures are unbounded or touch at one point. As an application, we give a version of the Stieltjes theorem in the context of simultaneous Hermite-Pade approximation.

• 出版日期2011-6