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
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
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
Notes:
Mathematics

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.