Revista Matemática Iberoamericana

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Volume 16, Issue 2, 2000, pp. 331–349
DOI: 10.4171/RMI/277

Published online: 2000-08-31

Construction of functions with prescribed Hölder and chirp exponents

Stéphane Jaffard[1]

(1) Université Paris Est, Créteil, France

We show that the Hölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general Hölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients; the optimality is the direct consequence of a general method we introduce in order to obtain lower bounds on the dimension of some fractal sets.

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Jaffard Stéphane: Construction of functions with prescribed Hölder and chirp exponents. Rev. Mat. Iberoam. 16 (2000), 331-349. doi: 10.4171/RMI/277