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Scaling exponents of self-similar functions and wavelet analysis
Author(s):
Koichi
Saka
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1035-1045.
MSC (2000):
Primary 28A80;
Secondary 42C40
Posted:
November 19, 2004
MathSciNet review:
2117204
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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:
10.1090/S0002-9939-04-07806-2
PII:
S 0002-9939(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
Posted:
November 19, 2004
Communicated by:
David R. Larson
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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