Multiple orthogonal polynomials
Multiple orthogonal polynomials
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DOI：
10.1016/s0377-0427(98)00175-7
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发表时间：
1998-11
影响因子：
2.4
通讯作者：
A. Aptekarev
中科院分区：
文献类型：
--
作者：
A. Aptekarev
将调查多个正交多项式的结果。多重正交多项式与 Hermite-Padé 近似密切相关，通常也称为 Hermite-Padé 多项式。将特别关注多重正交多项式的应用以及一般多重正交多项式的两个模型族（称为 Angelesco 和 Nikishin 系统）的解析理论。在这些应用中，数论、特殊函数和非对称带算子的谱分析将受到重点关注。在解析理论中，将回顾多个正交多项式渐近研究的结果和方法。将提出 Nikishin 系统的多个正交多项式的强渐近性的新结果。
Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite-Padé approximants and often they are also called Hermite-Padé polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angelesco and Nikishin systems. Among the applications the number theory, special functions and spectral analysis of nonsymmetric band operators will be highlighted. In the analytic theory results and methods for the study of multiple orthogonal polynomials asymptotics will be reviewed. New results on strong asymptotics of multiple orthogonal polynomials for Nikishin system will be presented.