Scaling exponents of self-similar functions and wavelet analysis

Author:
Koichi Saka

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1035-1045

MSC (2000):
Primary 28A80; Secondary 42C40

Published electronically:
November 19, 2004

MathSciNet review:
2117204

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give estimations of the pointwise scaling exponents of self-similar functions on the -dimensional Euclidean space . 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 , 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:
saka@math.akita-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07806-2

Keywords:
Self-similar functions,
scaling exponents,
wavelet analysis

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

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.