关于矩阵值Stieltjes函数的特殊子类
On Matrix-Valued Stieltjes Functions with an Emphasis on Particular Subclasses
摘要：
本文研究一类特殊的$q\times q$矩阵值函数，它们在$\mathbb{C}\setminus[α,+\infty)$中是全纯的，其中$α$是任意的实数.这些类是Kats和Krein [17]以及Krein和Nudelman [19]研究的全纯复值函数类的推广。这些函数与区间$[α,+\infty)$上的截断矩阵Stieltjes问题密切相关。通过整表示这些类的特征。特别强调的是放在这些矩阵值函数的Moore-Penrose逆的讨论。
英文摘要：
The paper deals with particular classes of $q\times q$ matrix-valued functions which are holomorphic in $\mathbb{C}\setminus[α,+\infty)$, where $α$ is an arbitrary real number. These classes are generalizations of classes of holomorphic complex-valued functions studied by Kats and Krein [17] and by Krein and Nudelman [19]. The functions are closely related to truncated matricial Stieltjes problems on the interval $[α,+\infty)$. Characterizations of these classes via integral representations are presented. Particular emphasis is placed on the discussion of the Moore-Penrose inverse of these matrix-valued functions.
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