Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Volume 130 / 1998

Simeon Reich, David Shoikhet Studia Mathematica 130 (1998), 231-244 DOI: 10.4064/sm-130-3-231-244


Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.


  • Simeon Reich
  • David Shoikhet

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