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

Abstract

The paper deals with particular classes of q×q matrix-valued functions which are holomorphic in \(\mathbb{C}\backslash [\alpha, +\infty)\), 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+∞). 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.