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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Scaling exponents of self-similar functions and wavelet analysis
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by Koichi Saka PDF
Proc. Amer. Math. Soc. 133 (2005), 1035-1045 Request permission


In this paper we give estimations of the pointwise scaling exponents of self-similar functions on the $n$-dimensional Euclidean space ${\mathbb R}^{n}$. These estimations are derived by using a technique based on wavelet analysis. Examples of such self-similar functions include indefinite integrals of self-similar measures on ${\mathbb R}$, and they also include widely oscillatory functions (e.g. the Takagi function, the Weierstrass function and Lévy’s function). Pointwise scaling exponents provide an objective description of an irregularity of a function at a point. Our results are applied to compute the scaling exponents of several oscillatory functions.
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Additional Information
  • Koichi Saka
  • Affiliation: Department of Mathematics, Akita University, Akita, 010-8502 Japan
  • Email:
  • Received by editor(s): April 25, 2001
  • Received by editor(s) in revised form: July 8, 2003
  • Published electronically: November 19, 2004
  • Communicated by: David R. Larson
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1035-1045
  • MSC (2000): Primary 28A80; Secondary 42C40
  • DOI:
  • MathSciNet review: 2117204