On Reproducing Kernel Spaces, J Unitary Matrix Functions, Interpolation and Displacement Rank

  • Harry Dym
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 40/41)

Abstract

In this paper structured reproducing kernel Hilbert spaces are used to solve matrix versions of a number of classical interpolation problems. Enroute a characterization of a class of such spaces which originates with de Branges is reformulated in terms of matrix equations of the Liapunov and Stein type in the finite dimensional case. Some generalizations to indefinite inner product spaces are also formulated. Finally it is shown that every invertible Hermitean matrix with displacement rank m is the Gram matrix of a “chain” of m × 1 vector valued functions in a suitably defined reproducing kernel Pontryagin space.

Keywords

Induction Hypothesis Matrix Equation Interpolation Problem Reproduce Kernel Hilbert Space Open Nonempty Subset 
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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Harry Dym
    • 1
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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