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Hausdorff dimension of the graphs of the classical Weierstrass functions

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 نشر من قبل Weixiao Shen
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Weixiao Shen




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We show that the graph of the classical Weierstrass function $sum_{n=0}^infty lambda^n cos (2pi b^n x)$ has Hausdorff dimension $2+loglambda/log b$, for every integer $bge 2$ and every $lambdain (1/b,1)$. Replacing $cos(2pi x)$ by a general non-constant $C^2$ periodic function, we obtain the same result under a further assumption that $lambda b$ is close to $1$.



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