Average distances on self-similar sets and higher order average distances of self-similar measures

D. Allen; H. Edwards; Scott Harper; Lars Ole Ronnow Olsen

doi:10.1007/s00209-016-1826-3

Average distances on self-similar sets and higher order average distances of self-similar measures

D. Allen, H. Edwards, Scott Harper, Lars Ole Ronnow Olsen

Pure Mathematics

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

Abstract

The purpose of this paper is twofold: (1) We study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of in ℝ.

Original language	English
Pages (from-to)	287-324
Number of pages	38
Journal	Mathematische Zeitschrift
Volume	287
Issue number	1-2
Early online date	29 Dec 2016
DOIs	https://doi.org/10.1007/s00209-016-1826-3
Publication status	Published - Oct 2017

Keywords

Self-similar set
Self-similar measures
Average distance
Moments
Mellin transform

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10.1007/s00209-016-1826-3Licence: CC BY

Allen_2016_Average_MZ_CC
Copyright The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Cite this

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KW - Self-similar set

KW - Self-similar measures

KW - Average distance

KW - Moments

KW - Mellin transform

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Average distances on self-similar sets and higher order average distances of self-similar measures

Abstract

Keywords

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