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Holder Regularity of mu-Similar Functions

Abstract : Given a positive measure mu, d contractions on [0,1] and a function g on a"e, we are interested in function series F that we call "mu-similar functions" associated with mu, 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 mu-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 mu-similar functions. We also try to relate the multifractal properties of mu to those of F and to develop a multifractal formalism (based on oscillation methods) associated with F.
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Submitted on : Tuesday, May 1, 2012 - 9:39:07 PM
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Moez Ben Abid, Stephane Seuret. Holder Regularity of mu-Similar Functions. Constructive Approximation, Springer Verlag, 2010, 31 (1), pp.69--93. ⟨10.1007/s00365-009-9042-6⟩. ⟨hal-00693124⟩



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