Long proofs of two carlson–schneider type inertia theorems

Harry Dym, Motke Porat

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

This expository note is devoted to a discussion of the equivalence of inertia theorems of the Carlson–Schneider type with the existence of finitedimensional reproducing kernel Krein spaces of the de Branges type. The first five sections focus on an inertia theorem connected with a Lyapunov equation. A sixth supplementary section sketches an analogous treatment of the Stein equation. The topic was motivated by a question raised by Leonid Lerer.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages107-125
Number of pages19
DOIs
StatePublished - 1 Jan 2013
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
Volume237
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Factorization of rational matrixvalued functions
  • Finite-dimensional de Branges–Krein spaces
  • Inertia theorems
  • Lyapunov–Stein equations
  • Realization theory
  • Reproducing kernel spaces

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