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On the Fractional Fractal Analysis of Multivariate Pointwise Lipschitz Oscillating Regularity |
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PP: 2215-2226 |
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doi:10.18576/isl/120602
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Author(s) |
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Ines Ben Omrane,
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Abstract |
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| Classical Lipschitz regularity does not allow to capture possible different oscillating directional pointwise regularity behaviors in coordinate axes of functions f on Rd, d ≥ 2. To overcome this drawback, we use iterated fractional primitives to introduce a notion of multivariate pointwise Lipschitz oscillating regularity. We show a characterization in hyperbolic wavelet bases. As an application, we obtain the fractal print dimension of a given set of multivariate Lipschitz oscillating regularity, from the knowledge of fractional axes oscillating spaces to which f belongs.
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