Construction of continuous functions with prescribed local regularity
Khalid, Daoudi; Lévy Véhel, Jacques; Yves, Meyer (1998), Construction of continuous functions with prescribed local regularity, Constructive Approximation, 14, 3, p. 349-385. http://dx.doi.org/10.1007/s003659900078
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.inria.fr/inria-00593268/fr/
Journal nameConstructive Approximation
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Abstract (EN)In this work we investigate both from a theoretical and a practical point of view the following problem: Let s be a function from [0;1] to [0;1]. Under which conditions does there exist a continuous function f from [0;1] to IR such that the regularity of f at x, measured in terms of Hölder exponent, is exactly s(x), for all x [0;1]? We obtain a necessary and sufficient condition on s and give three constructions of the associated function f. We also examine some extensions, as for instance conditions on the box or Tricot dimension or the multifractal spectrum of these functions. Finally we present a result on the "size" of the set of functions with prescribed local regularity.
Subjects / Keywordscontinuous functions
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