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Book Sections Year : 2017

New exponents for pointwise singularity classification

Abstract

We introduce new tools for pointwise singularity classification: We investigate the properties of the two-variable function which is defined at every point as the p-exponent of a fractional integral of order t; new exponents are derived which are not of regularity type but give a more precise description of the behavior of the function near a singularity. We revisit several classical examples (deterministic and random) of multifractal functions for which the additional information supplied by this classification is derived. Finally, a new example of multifractal function is studied, where these exponents prove pertinent.
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Dates and versions

hal-03116306 , version 1 (20-01-2021)

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Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt. New exponents for pointwise singularity classification. Seuret, Stéphane; Barral, Julien. Recent Developments in Fractals and Related Fields: Conference on Fractals and Related Fields III, FARF3 2015: Recent Developments in Fractals and Related Fields, Birkhäuser, pp.1-37, 2017, Trends in Mathematics book series (TM), 978-3-319-57803-3. ⟨10.1007/978-3-319-57805-7_1⟩. ⟨hal-03116306⟩
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