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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Hausdorff dimension of graphs
of Weierstrass functions


Author: Brian R. Hunt
Journal: Proc. Amer. Math. Soc. 126 (1998), 791-800
MSC (1991): Primary 28A80, 26A30, 28A78; Secondary 58F12
MathSciNet review: 1452806
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Abstract: The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.


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Additional Information

Brian R. Hunt
Affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431
Email: bhunt@ipst.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04387-1
PII: S 0002-9939(98)04387-1
Received by editor(s): September 3, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society