On Matrix-Valued Stieltjes Functions with an Emphasis on Particular Subclasses

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.

No reviews yet.

No comments yet.