Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Simeon Reich; David Shoikhet

Studia Mathematica (1998)

  • Volume: 130, Issue: 3, page 231-244
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Reich, Simeon, and Shoikhet, David. "Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains." Studia Mathematica 130.3 (1998): 231-244. <http://eudml.org/doc/216555>.

@article{Reich1998,
abstract = {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.},
author = {Reich, Simeon, Shoikhet, David},
journal = {Studia Mathematica},
keywords = {hyperbolic convex domain; complex Banach space; quasi-regular point; averaged mapping; power convergent},
language = {eng},
number = {3},
pages = {231-244},
title = {Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains},
url = {http://eudml.org/doc/216555},
volume = {130},
year = {1998},
}

TY - JOUR
AU - Reich, Simeon
AU - Shoikhet, David
TI - Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains
JO - Studia Mathematica
PY - 1998
VL - 130
IS - 3
SP - 231
EP - 244
AB - 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.
LA - eng
KW - hyperbolic convex domain; complex Banach space; quasi-regular point; averaged mapping; power convergent
UR - http://eudml.org/doc/216555
ER -

References

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