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On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials
Journal of Difference Equations and Applications ( IF 1.1 ) Pub Date : 2021-02-17 , DOI: 10.1080/10236198.2021.1887160
S. M. Zagorodnyuk 1
Affiliation  

For every system {pn(z)}n=0 of OPRL or OPUC, we construct Sobolev orthogonal polynomials yn(z), with explicit integral representations involving pn. Two concrete families of Sobolev orthogonal polynomials (depending on an arbitrary number of complex parameters) which are generalized eigenvalues of a difference operator (in n) and generalized eigenvalues of a differential operator (in z) are given. We define suitable Sobolev spaces with matrix weights and consider measurable factorizations of weights. Applications of a general connection between Sobolev orthogonal polynomials and orthogonal systems of functions in the direct sum of scalar Lμ2 spaces are discussed.



中文翻译:

关于某些具有矩阵权重和经典类型Sobolev正交多项式的Sobolev空间

对于每个系统 {pñž}ñ=0 关于OPRL或OPUC,我们构造Sobolev正交多项式 ÿñž,其中涉及明确的整数表示 pñ。给出了两个具体的Sobolev正交多项式族(取决于任意数量的复杂参数),它们是差分算子的广义特征值(在n中)和微分算子的广义特征值(在z中)。我们用矩阵权重定义合适的Sobolev空间,并考虑权重的可测量因式分解。Sobolev正交多项式与函数正交系统之间的一般联系在标量直接和中的应用大号μ2个 讨论了空格。

更新日期:2021-03-22
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