JournalsrmiVol. 16, No. 2pp. 331–349

Construction of functions with prescribed Hölder and chirp exponents

  • Stéphane Jaffard

    Université Paris Est, Créteil, France
Construction of functions with prescribed Hölder and chirp exponents cover
Download PDF

Abstract

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.

Cite this article

Stéphane Jaffard, Construction of functions with prescribed Hölder and chirp exponents. Rev. Mat. Iberoam. 16 (2000), no. 2, pp. 331–349

DOI 10.4171/RMI/277