The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems
The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems
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DOI：
10.1088/0266-5611/26/5/055009
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发表时间：
2009-11
期刊：
影响因子：
2.1
通讯作者：
C. Alvarez-Fernandez;U. Fidalgo;Manuel Mañas
中科院分区：
文献类型：
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作者：
C. Alvarez-Fernandez;U. Fidalgo;Manuel Mañas
研究了二维多分量户田方程族与矩阵正交多项式和双正交多项式的关系。考虑了该族的多级Hankel约化，并研究了相应的广义矩阵正交多项式。特别是，对于这些多项式，我们考虑的递归关系，并为秩1的权重与混合型的多个正交多项式的关系与II型规范化和相应的链接与黎曼-希尔伯特问题。
We consider the relation of the multicomponent 2D Toda hierarchy with the matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polynomials are studied. In particular, for these polynomials we consider the recursion relations, and for rank 1 weights its relation with multiple orthogonal polynomials of mixed type with a type II normalization and the corresponding link with a Riemann–Hilbert problem.