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A Unified Approach for Nondifferentiable Functions

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
182
Issue
1
Identifiers
DOI: 10.1006/jmaa.1994.1071

Abstract

Abstract Let ψ( x) denote the distance between x and the nearest integer, and fix 0 < a < 1, ab > 1, where b is not necessarily an integer. Then for any sequence θ n of phases, the function f( x) = ∑ ∞ n=0 a n ψ( b nx + θ n ) has no right (left) derivative at any point x and 2 + (log a/log b) is the box-counting dimension of the graph of f. The crucial step is to obtain the smallest Lipschitz class to which ƒ belongs.

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