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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)287-324
Number of pages38
JournalMathematische Zeitschrift
Volume287
Issue number1-2
Early online date29 Dec 2016
DOIs
Publication statusPublished - Oct 2017

Keywords

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

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