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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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A rough differentiable function
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by Bernd Kirchheim and Paul F.X. Müller PDF
Proc. Amer. Math. Soc. 136 (2008), 3875-3881

Abstract:

A real-valued continuously differentiable function $f$ on the unit interval is constructed such that \[ \sum _{k=1}^\infty \beta _f (x, 2^{-k} ) = \infty \] holds for every $x \in [0,1].$ Here $\beta _f (x, 2^{-k} )$ measures the distance of $f$ to the best approximating linear function at scale $2^{-k}$ around $x$.
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Additional Information
  • Bernd Kirchheim
  • Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom
  • Paul F.X. Müller
  • Affiliation: Institut für Analysis und Numerik, J. Kepler Universität Linz, A-4040 Linz, Austria
  • MR Author ID: 240120
  • Email: pfxm@bayou.uni-linz.ac.at
  • Received by editor(s): May 17, 2002
  • Received by editor(s) in revised form: July 18, 2007
  • Published electronically: June 26, 2008
  • Communicated by: David Preiss
  • © Copyright 2008 by the authors
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3875-3881
  • MSC (2000): Primary 26A16, 30D55, 26A24, 30C99
  • DOI: https://doi.org/10.1090/S0002-9939-08-09322-2
  • MathSciNet review: 2425727