Keller G (2015)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2015
Book Volume: 53
Pages Range: 169-181
Let $W_{lambda,b}(x)=sum_{n=0}^inftylambda^n g(b^n x)$ where $bgeqslant2$ is an integer and $g(u)=cos(2pi u)$ (classical Weierstrass function). Building on work by Ledrappier (1992), Bar'ansky, B'ar'any and Romanowska (2013) and Tsujii (2001), we provide an elementary proof that the Hausdorff dimension of $W_{lambda,b}$ equals $2+frac{loglambda}{log b}$ for all $lambdain(lambda_b,1)$ with a suitable $lambda_b<1$. This reproduces results by Bar'ansky, B'ar'any and Romanowska without using the dimension theory for hyperbolic measures of Ledrappier and Young (1985,1988), which is replaced by a simple telescoping argument together with a recursive multi-scale estimate.
APA:
Keller, G. (2015). An elementary proof for the dimension of the graph of the classical Weierstrass function. Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 53, 169-181.
MLA:
Keller, Gerhard. "An elementary proof for the dimension of the graph of the classical Weierstrass function." Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques 53 (2015): 169-181.
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