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

Allen, D.; Edwards, H.; Harper, S.; Olsen, Lars Ole Ronnow

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Date

10/2017

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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.

Citation

Allen , D , Edwards , H , Harper , S & Olsen , L O R 2017 , ' Average distances on self-similar sets and higher order average distances of self-similar measures ' , Mathematische Zeitschrift , vol. 287 , no. 1-2 , pp. 287-324 . https://doi.org/10.1007/s00209-016-1826-3

Publication

Mathematische Zeitschrift

Status

Peer reviewed

DOI

https://doi.org/10.1007/s00209-016-1826-3

ISSN

0025-5874

Type

Journal article

Rights

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.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/10069