论文标题
在某些具有基质重量和经典类型Sobolev正交多项式的Sobolev空间上
On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials
论文作者
论文摘要
对于每个系统$ \ {p_n（z）\} _ {n = 0}^\ oprl或opuc的infty $，我们构建了Sobolev orthoconal polyenmials $ y_n（z）$，具有涉及$ p_n $的明显积分表示。 Sobolev正交多项式的两个混凝土家族（取决于任意数量的复杂参数），它们是差异操作员的广义特征值（以$ n $为单位），并给出了差异运算符的广义特征值（以$ n $）。讨论了Sobolev正交多项式和函数的正交系统之间的一般连接在标量$ l^2_μ$空间中的应用。
For every system $\{ p_n(z) \}_{n=0}^\infty$ of OPRL or OPUC, we construct Sobolev orthogonal polynomials $y_n(z)$, with explicit integral representations involving $p_n$. 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 $n$) are given. Applications of a general connection between Sobolev orthogonal polynomials and orthogonal systems of functions in the direct sum of scalar $L^2_μ$ spaces are discussed.
