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  1. Article

    Open Access

    Hyperbolic Wavelet Analysis of Classical Isotropic and Anisotropic Besov–Sobolev Spaces

    In this paper we introduce new function spaces which we call anisotropic hyperbolic Besov and Triebel-Lizorkin spaces. Their definition is based on a hyperbolic Littlewood-Paley analysis involving an anisotrop...

    Martin Schäfer, Tino Ullrich… in Journal of Fourier Analysis and Applications (2021)

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  2. No Access

    Chapter

    On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time

    From a theoretical perspective, scale invariance, or simply scaling, can fruitfully be modeled with classes of multifractal stochastic processes, designed from positive multiplicative martingales (or cascades)...

    Béatrice Vedel, Herwig Wendt, Patrice Abry… in Dependence in Probability and Statistics (2010)

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    Article

    Wavelet Bases for Confinements of the Infrared Divergence

    We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces $\dot{H}^{s}(\mathbb{R...

    Béatrice Vedel in Journal of Fourier Analysis and Applications (2009)

  4. No Access

    Chapter and Conference Paper

    Wavelet Decomposition of Measures: Application to Multifractal Analysis of Images

    We show the relevance of multifractal analysis for some problems in image processing. We relate it to the standard question of the determination of correct function space settings. We show why a scale-invarian...

    Patrice Abry, Stéphane Jaffard… in Unexploded Ordnance Detection and Mitigati… (2009)