Geometrical dimension versus smoothness |
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| Authors: | Anca Deliu Björn Jawerth |
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| Affiliation: | 1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA
2. Department of Mathematics, University of South Carolina, 29208, Columbia, South Carolina, USA
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| Abstract: | We study the relation between geometric dimension and smoothness, and give a precise characterization of the fractal dimension of the graph of a function in terms of smoothness classes of functions. We also express the fractal dimension in terms of different classical oscillation measures and in terms of wavelet expansions. |
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