Ergodic Methods for the Construction of Holomorphic Retractions

  • Victor Khatskevich
  • Simeon Reich
  • David Shoikhet
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)


Let D be a bounded convex domain in a complex Banach space, and let F be a holomorphic self-mapping of D with a nonempty fixed point set. In this paper we study the flow generated by the mapping IF on D, and use the asymptotic behavior of its Cesàro averages to construct a holomorphic retraction of D onto the fixed point set of F.


Null Point Complex Banach Space Bounded Convex Domain Bounded Holomorphic Mapping Local Uniform Convergence 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Victor Khatskevich
    • 1
  • Simeon Reich
    • 2
  • David Shoikhet
    • 1
  1. 1.Department of Applied MathematicsInternational College of TechnologyKarmielIsrael
  2. 2.Department of MathematicsThe Technion - Israel Institute of TechnologyHaifaIsrael

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