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On Realizations of Rational Matrix Functions of Several Complex Variables

  • M. F. Bessmertnyĭ
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 134)

Abstract

Holomorphic functions of one complex variable with a non-negative imaginary part, and the related classes of J-contractive matrix functions (contractive in a space with an indefinite metric, defined in a standard way by a hermitian matrix J such that J 2 = I) were actively studied by many mathematicians in the past years. A series of problems of mathematical analysis and its applications lead to the necessity of studying analogous classes of holomorphic functions of several complex variables. Holomorphic functions with a non-negative imaginary part in a tubular domain over a cone and in the polydisk were studied by V.S. Vladimirov (see [Vla2], [V1a5]–[V1a8]) and by Vladimirov and Drozhzhinov [29]. In bounded strictly star-shaped domains, and in particular in the classical symmetric domains, they were studied by L.A. Aizenberg and Sh.A. Dautov [1]. W. Rudin (see [Rud]) gives a “parametrical” representation of scalar rational inner functions in the polydisk \(\mathbb{D}^n \). The parameter is an arbitrary polynomial non-vanishing in \(\mathbb{D}^n \).

Keywords

Rational Function Holomorphic Function Matrix Function English Trans Rational Matrix Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • M. F. Bessmertnyĭ
    • 1
  1. 1.Department of Mathematics Faculty of PhysicsKharkov National UniversityKharkovUkraina

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