Result: On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies
Title:
On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies
Authors:
Source:
Nonlinearity (Bristol. Print). 25(1):193-209
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 15 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions réelles, Real functions, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Dimension Hausdorff, Hausdorff dimension, Dimensión Hausdorff, Dimension fractale, Fractal dimension, Dimensión fractal, Fonction Lipschitz, Lipschitz function, Función Lipschitz, Fonction Weierstrass, Weierstrass functions, Fonction forme, Shape function, Función forma, Fonction périodique, Periodic function, Función periódica, Fonction réelle, Real function, Función real, Physique mathématique, Mathematical physics, Física matemática, 26XX, Graphe, Graph
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.25413660
Database:
PASCAL Archive
Further Information
We determine the Hausdorff and box dimension of the fractal graphs of some Weierstrass-type functions of the form f(x) = ∑∞n=1 an g(bnx+θn), where g is a periodic Lipschitz real function and an+1/an → 0, bn+1/bn → ∞ as n → ∞. Moreover, for any 1 ≤ H ≤ B ≤ 2 we provide examples of such functions with dimH(graph f) = dimB(graph f) = H, dimB(graph f) = B.