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Singularity Spectrum of Generic alpha-Holder Regular Functions After Time Subordination

Abstract : A question of Yves Meyer motivated the research concerning "time" subordinations of real functions. Denote by beta(alpha)(1) the metric space of functions with Lipschitz constant 1 defined on [0,1], equipped with the complete metric defined via the supremum norm. Given a function g is an element of beta(alpha)(1)one obtains a time subordination of g simply by considering the composite function Z=gau < f, where faa"(3):={f:f(0)=0, f(1)=1 and f is a continuous nondecreasing function on [0,1]}. The metric space epsilon = M X beta(alpha)(1) equipped with the product supremum metric is a complete metric space. In this paper for all alpha a[0,1) multifractal properties of gau < f are investigated for a generic (typical) element (f,g)aa"degrees (alpha) . In particular we determine the generic Holder singularity spectrum of gau < f.
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Zoltan Buczolich, Stephane Seuret. Singularity Spectrum of Generic alpha-Holder Regular Functions After Time Subordination. Journal of Fourier Analysis and Applications, Springer Verlag, 2011, 17 (3), pp.457--485. ⟨10.1007/s00041-010-9140-7⟩. ⟨hal-00692988⟩



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