论文标题
在矩阵sobolev空间中的自变量乘法运算符上
On the multiplication operator by an independent variable in matrix Sobolev spaces
论文作者
论文摘要
我们研究了通过矩阵sobolev space $ w^2（m）$中的自变量乘以乘法的运算符$ \ Mathcal {a} $。在$ [a，b] $的有限度量的情况下，$（2 \ times 2）$和$（3 \ times 3）$全等级的真实连续矩阵权重表明操作员$ \ mathcal {a} $是同样的。即，在较大的空间中存在两个对称操作员$ \ MATHCAL {B} $和$ \ MATHCAL {C} $，因此$ \ Mathcal {a} f = \ Mathcal {c} \ Mathcal {c} \ Mathcal {b}作为推论，我们为相关的Sobolev正交多项式获得了一些新的正交条件。这些条件涉及两个不确定度量空间中的对称操作员。
We study the operator $\mathcal{A}$ of multiplication by an independent variable in a matrix Sobolev space $W^2(M)$. In the cases of finite measures on $[a,b]$ with $(2\times 2)$ and $(3\times 3)$ real continuous matrix weights of full rank it is shown that the operator $\mathcal{A}$ is symmetrizable. Namely, there exist two symmetric operators $\mathcal{B}$ and $\mathcal{C}$ in a larger space such that $\mathcal{A} f = \mathcal{C} \mathcal{B}^{-1} f$, $f\in D(\mathcal{A})$. As a corollary, we obtain some new orthogonality conditions for the associated Sobolev orthogonal polynomials. These conditions involve two symmetric operators in an indefinite metric space.
