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Hölder Regularity of μ-Similar Functions

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Abstract

Given a positive measure μ, d contractions on [0,1] and a function g on ℝ, we are interested in function series F that we call “μ-similar functions” associated with μ, g and the contractions. These series F are defined as infinite sums of rescaled and translated copies of the function g, the dilation and translations depending on the choice of the contractions. The class of μ-similar functions F intersects the classes of self-similar and quasi-self-similar functions, but the heterogeneity we introduce in the location of the copies of g make the class much larger.

We study the convergence and the global and local regularity properties of the μ-similar functions. We also try to relate the multifractal properties of μ to those of F and to develop a multifractal formalism (based on oscillation methods) associated with F.

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Authors and Affiliations

  1. Institut Supérieur d’Informatique et des Technologies de Communication, G.P.1 Hammam Sousse 4011, Sousse, Tunisia

    Moez Ben Abid

  2. LAMA—CNRS UMR 8050, Université Paris-Est, 61, avenue du Général de Gaulle, 94040, Creteil Cedex, France

    Stéphane Seuret

Authors
  1. Moez Ben Abid
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  2. Stéphane Seuret
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Correspondence to Moez Ben Abid.

Additional information

Communicated by Stephane Jaffard.

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Ben Abid, M., Seuret, S. Hölder Regularity of μ-Similar Functions. Constr Approx 31, 69–93 (2010). https://doi.org/10.1007/s00365-009-9042-6

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  • DOI: https://doi.org/10.1007/s00365-009-9042-6

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