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
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Article accepté pour publication ou publiéExternal document link
http://hal.inria.fr/inria-00593268/fr/Date
1998Journal name
Constructive ApproximationVolume
14Number
3Publisher
Springer
Pages
349-385
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Show full item recordAbstract (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 / Keywords
continuous functionsRelated items
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