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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Local and non-local Dirichlet forms on the Sierpiński carpet
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by Alexander Grigor’yan and Meng Yang PDF
Trans. Amer. Math. Soc. 372 (2019), 3985-4030 Request permission

Abstract:

We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpiński carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.
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Additional Information
  • Alexander Grigor’yan
  • Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
  • MR Author ID: 203816
  • Email: grigor@math.uni-bielefeld.de
  • Meng Yang
  • Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
  • Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
  • MR Author ID: 1226000
  • Email: ymeng@math.uni-bielefeld.de, meng-yang13@mails.tsinghua.edu.cn
  • Received by editor(s): August 21, 2017
  • Received by editor(s) in revised form: July 12, 2018
  • Published electronically: May 9, 2019
  • Additional Notes: The authors were supported by SFB701 and SFB1283 of the German Research Council (DFG)
    The second author is the corresponding author
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 3985-4030
  • MSC (2010): Primary 28A80
  • DOI: https://doi.org/10.1090/tran/7753
  • MathSciNet review: 4009425