Hausdorff dimension of scale-sparse Weierstrass-type functions

Abel Carvalho

Abel Carvalho

Fundamenta Mathematicae, Tome 215 (2011), p. 1-13 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim of this paper is to calculate (deterministically) the Hausdorff dimension of the scale-sparse Weierstrass-type functions $W_{s} (x) : = \sum_{j \geq 1} ρ^{- γ^{j} s} g (ρ^{γ^{j}} x + θ_{j})$ , where ρ > 1, γ > 1 and 0 < s < 1, and g is a periodic Lipschitz function satisfying some additional appropriate conditions.

Publié le : 2011-01-01

Zbl 1235.28007

EUDML-ID : urn:eudml:doc:283355

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-1-1,
     author = {Abel Carvalho},
     title = {Hausdorff dimension of scale-sparse Weierstrass-type functions},
     journal = {Fundamenta Mathematicae},
     volume = {215},
     year = {2011},
     pages = {1-13},
     zbl = {1235.28007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-1-1}
}

Abel Carvalho. Hausdorff dimension of scale-sparse Weierstrass-type functions. Fundamenta Mathematicae, Tome 215 (2011) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm213-1-1/