# A note on the Hausdorff dimension of general sums of pulses graphs

Rendiconti del Circolo Matematico di Palermo

, Volume 60, Issue 3, pp 469–476

First Online: 15 July 2011Received: 28 February 2011Accepted: 08 March 2011

Abstract

In this work we study the some general fractal sums of pulses defined in ℝ by: $$Ft =\sum^{+\infty} {n=1}a nG\lambda n^{-1}t-X n$$ where an, λn two positive scalar sequences such that ∑an is divergent, and λn is non-increasing to 0, G is an elementary bump and Xn are independent random variables uniformly distributed on a sufficiently large domain Ω. We investigate the Hausdorff dimension of the graph of G and in particular we answer a question given by Tricot in Courbes et dimensions fractales, Springer, Berlin, 1995.KeywordsHausdorff dimension Sum of pulses Box dimension Mathematics Subject Classification 200060D05 60G99 28A80  Download to read the full article text

Author: Enrique de Amo - Imen Bhouri - Juan Fernández-Sánchez