Construction of functions with prescribed Hölder and chirp exponents
type: Item
instance of: scholarly article
title: Construction of functions with prescribed Hölder and chirp exponents
zbMATH Open document ID: 0987.42024
DOI: 10.4171/RMI/277
author: Stéphane Jaffard
published in: Revista Matemática Iberoamericana
publication date: 2001-02-11T00:00:00Z
full work available at URL: https://eudml.org/doc/39605
review text: Summary: 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.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1563251
zbMATH Keywords: Hölder exponent
zbMATH Keywords: chirp exponent
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: orthonormal wavelet coefficients
zbMATH Keywords: fractal sets
MaRDI profile type: Publication
OpenAlex ID: W2078610823
description: scientific article; zbMATH DE number 1563251