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Journal of Mathematical Sciences

, Volume 234, Issue 1, pp 82–97 | Cite as

Factorization of generalized γ-generating matrices

  • Olena Sukhorukova
Article

Abstract

The class of γ-generating matrices and its subclasses of regular and singular γ-generating matrices were introduced by D. Z. Arov in [8], where it was shown that every γ-generating matrix admits an essentially unique regular–singular factorization. The class of generalized γ-generating matrices was introduced in [14, 20]. In the present paper, subclasses of singular and regular generalized –generating matrices are introduced and studied. As the main result, a theorem of existence of the regular–singular factorization for a rational generalized γ-generating matrix is proved.

Keywords

γ-generating matrices J-inner matrix-valued function denominator associated pair generalized Schur class reproducing kernel space Potapov–Ginzburg transform Krein–Langer factorization 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dragomanov National Pedagogical UniversityKievUkraine

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