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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convergence of refinement schemes on metric spaces
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by Oliver Ebner PDF
Proc. Amer. Math. Soc. 141 (2013), 677-686 Request permission

Abstract:

We analyze the convergence of iterative refinement processes on metric spaces, imposing the principle of contractivity to obtain convergence criteria. As a major result, we show that on Hadamard spaces a wide natural class of contractible barycentric subdivision schemes converges.
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Additional Information
  • Oliver Ebner
  • Affiliation: Institute of Geometry, TU Graz, Kopernikusgasse 24/IV, A-8010 Graz, Austria
  • Email: o.ebner@tugraz.at
  • Received by editor(s): March 25, 2011
  • Received by editor(s) in revised form: June 30, 2011
  • Published electronically: June 7, 2012
  • Additional Notes: The author was supported by the Austrian science fund, grant W1230.
  • Communicated by: Walter Van Assche
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 677-686
  • MSC (2010): Primary 53C23, 65D17
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11331-0
  • MathSciNet review: 2996972