Construction of functions with prescribed Hölder and Chirp exponents

Autores: Stéphane Jaffard
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 16, Nº 2, 2000, págs. 331-350
Idioma: inglés
DOI: 10.4171/rmi/277
Títulos paralelos:
- Construcción de funciones con exponentes Hölder y chirp prescritos
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Resumen
- We show that the Hölder exponent and the chirp exponent of a function can be precribed 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 precribed outisde 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.