论文标题
Hessenberg-Sobolev矩阵和最爱定理
Hessenberg-Sobolev Matrices and Favard type theorems
论文作者
论文摘要
我们研究某些非分类的下赫森伯格无限矩阵$ \ MATHCAL {G} $与正交多项式序列相对于Sobolev内部产品的存在。换句话说，我们扩展了众所周知的sobolev正交定理。我们在某些矩阵操作员方面表征了矩阵$ \ MATHCAL {G} $的结构和正式矩$ \ MATHCAL {M} _ {\ MATHCAL {G}} $的正式矩阵的结构。
We study the relation between certain non-degenerate lower Hessenberg infinite matrices $\mathcal{G}$ and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix $\mathcal{G}$ and the associated matrix of formal moments $\mathcal{M}_{\mathcal{G}}$ in terms of certain matrix operators.
