Summary
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.
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Demichel, Y. (2010). L p-Norms and Fractal Dimensions of Continuous Function Graphs. In: Barral, J., Seuret, S. (eds) Recent Developments in Fractals and Related Fields. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4888-6_10
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DOI: https://doi.org/10.1007/978-0-8176-4888-6_10
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