On matrix-valued Stieltjes functions with an emphasis on particular subclasses

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Abstract

The paper deals with particular classes of q×q matrix-valued functions which are holomorphic in ℂ\[α,+∞), 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.

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Fritzsche, B., Kirstein, B., & Mädler, C. (2017). On matrix-valued Stieltjes functions with an emphasis on particular subclasses. In Operator Theory: Advances and Applications (Vol. 259, pp. 301–352). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_15

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