# Construction of functions with prescribed Hölder and chirp exponents.

Revista Matemática Iberoamericana (2000)

- Volume: 16, Issue: 2, page 331-349
- ISSN: 0213-2230

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topJaffard, Stéphane. "Construction of functions with prescribed Hölder and chirp exponents.." Revista Matemática Iberoamericana 16.2 (2000): 331-349. <http://eudml.org/doc/39605>.

@article{Jaffard2000,

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.},

author = {Jaffard, Stéphane},

journal = {Revista Matemática Iberoamericana},

keywords = {Funciones continuas; Análisis armónico; Ondículas; Fractales; Hölder exponent; chirp exponent; Hausdorff dimension; orthonormal wavelet coefficients; fractal sets},

language = {eng},

number = {2},

pages = {331-349},

title = {Construction of functions with prescribed Hölder and chirp exponents.},

url = {http://eudml.org/doc/39605},

volume = {16},

year = {2000},

}

TY - JOUR

AU - Jaffard, Stéphane

TI - Construction of functions with prescribed Hölder and chirp exponents.

JO - Revista Matemática Iberoamericana

PY - 2000

VL - 16

IS - 2

SP - 331

EP - 349

AB - 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.

LA - eng

KW - Funciones continuas; Análisis armónico; Ondículas; Fractales; Hölder exponent; chirp exponent; Hausdorff dimension; orthonormal wavelet coefficients; fractal sets

UR - http://eudml.org/doc/39605

ER -

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