The Hausdorff dimension of pulse-sum graphs.

Kenneth John Falconer; Yann Demichel

doi:10.1017/S0305004107000321

The Hausdorff dimension of pulse-sum graphs.

Kenneth John Falconer, Yann Demichel

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider random functions formed as sums of pulses

F(t) = infinity Sigma n=1n(-alpha/D)G(n(1/D)(t- X-n)) (t is an element of R-D)

where X-n are independent random vectors, 0 < alpha < 1, and G is an elementary "pulse" or "bump". Typically such functions have fractal graphs and we find the Hausdorff dimension of these graphs using a novel variant on the potential theoretic method.

Original language	English
Pages (from-to)	145-155
Number of pages	11
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	143
DOIs	https://doi.org/10.1017/S0305004107000321
Publication status	Published - Jul 2007

Keywords

FRACTAL SUMS

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10.1017/S0305004107000321

Cite this

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AB - We consider random functions formed as sums of pulsesF(t) = infinity Sigma n=1n(-alpha/D)G(n(1/D)(t- X-n)) (t is an element of R-D)where X-n are independent random vectors, 0 < alpha < 1, and G is an elementary "pulse" or "bump". Typically such functions have fractal graphs and we find the Hausdorff dimension of these graphs using a novel variant on the potential theoretic method.

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DO - 10.1017/S0305004107000321

M3 - Article

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VL - 143

SP - 145

EP - 155

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -

The Hausdorff dimension of pulse-sum graphs.

Abstract

Keywords

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