Revista Matemática Iberoamericana
Full-Text PDF (250 KB) | Metadata | Table of Contents | RMI summary
Published online: 2000-08-31
Construction of functions with prescribed Hölder and chirp exponentsStéphane Jaffard (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.
No keywords available for this article.
Jaffard Stéphane: Construction of functions with prescribed Hölder and chirp exponents. Rev. Mat. Iberoam. 16 (2000), 331-349. doi: 10.4171/RMI/277