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On the Bessmertnyĭ Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes

  • Dmitry S. Kalyuzhnyĭ-Verbovetzkiĭ
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 157)

Abstract

We generalize our earlier results from [9] on the Bessmertnyĭ class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous operator-valued function with positive semidefinite operator coefficients, to the case of a product of open right matrix halfplanes. Several equivalent characterizations of this generalized Bessmertnyĭ class are presented. In particular, its intimate connection with the Agler-Schur class of holomorphic contractive operator-valued functions on the product of matrix unit disks is established.

Keywords

Several complex variables homogeneous positive holomorphic operator-valued functions product of matrix halfplanes long resolvent representations Agler-Schur class 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Dmitry S. Kalyuzhnyĭ-Verbovetzkiĭ
    • 1
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael

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