Convex invertible cones and positive real analytic functions

Nir Cohen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In this paper we study classical spaces of analytic functions which are convex cones and closed under the involution f → 1 / f . These include the spaces of positive real, positive real odd, and strictly positive real functions. These spaces are associated in the engineering literature with energy dissipation in the sense of Lyapunov. We discuss the geometric aspects of these spaces, in analogy with similar spaces in matrix theory which are also related to the matrix Lyapunov equation, stability and in view of a general theory of convex invertible cones.

Original languageEnglish
Pages (from-to)797-813
Number of pages17
JournalLinear Algebra and Its Applications
Issue number2-3
StatePublished - 1 Sep 2007


  • Convex invertible cones
  • Lyapunov matrix inclusion
  • Positive real functions

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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