Journal of Difference Equations and Applications ( IF 1.1 ) Pub Date : 2021-02-17 , DOI: 10.1080/10236198.2021.1887160 S. M. Zagorodnyuk 1
For every system of OPRL or OPUC, we construct Sobolev orthogonal polynomials , with explicit integral representations involving . 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 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 关于OPRL或OPUC,我们构造Sobolev正交多项式 ,其中涉及明确的整数表示 。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 讨论了空格。