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Stieltjes and inverse Stieltjes holomorphic families of linear relations and their representations

Volume 252 / 2020

Yury Arlinskiĭ, Seppo Hassi Studia Mathematica 252 (2020), 129-167 MSC: 47A06, 47A20, 47A48, 47A56, 47B25, 47B44. DOI: 10.4064/sm180714-12-3 Published online: 20 December 2019


We study analytic and geometric properties of Stieltjes and inverse Stieltjes families defined on a separable Hilbert space and establish various minimal representations for them by means of compressed resolvents of various types of linear relations. Also, attention is paid to some new peculiar properties of Stieltjes and inverse Stieltjes families, including an analog for the notion of inner functions which will be characterized in an explicit manner. In addition, families which admit different types of scale invariance properties are described. Two transformers that naturally appear in Stieltjes and inverse Stieltjes classes are introduced and their fixed points are identified.


  • Yury ArlinskiĭVolodymyr Dahl East Ukrainian
    National University
    pr. Central 59-A
    Severodonetsk, 93400, Ukraine
  • Seppo HassiDepartment of Mathematics and Statistics
    University of Vaasa
    P.O. Box 700
    65101 Vaasa, Finland

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