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.
Mathematics Subject Classification (2010). Primary 30E05, 47A57; Secondary 44A60.
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Fritzsche, B., Kirstein, B., Mädler, C. (2017). On Matrix-valued Stieltjes Functions with an Emphasis on Particular Subclasses. In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_15
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DOI: https://doi.org/10.1007/978-3-319-49182-0_15
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-49180-6
Online ISBN: 978-3-319-49182-0
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