Lp-Norms and Fractal Dimensions of Continuous Function Graphs

  • Yann Demichel
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We study the fractal dimensions of continuous function graphs and more general fractal parameters. They are all obtained from the L p -norms of some well-built operators. We give general results about these norms in the continuous and the discrete cases. For a function that is uniformly Hölderian, they allow us to estimate in a very easy way a large family of dimensional indices, like the box dimension and regularization dimension.


Regularization Dimension Fractal Index Uniform Probability Determine Function Riemann Function 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MAP5 - Laboratoire de Mathématiques Appliquées, Bureau 725C1Université Paris DescartesParis Cedex 06France

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