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

D. Allen; H. Edwards; S. Harper; L. 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, S. Harper, L. Olsen^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

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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 (Formula presented.), and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of (Formula presented.).

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

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

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10.1007/s00209-016-1826-3

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AU - Edwards, H.

AU - Harper, S.

AU - Olsen, L.

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AB - 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 (Formula presented.), and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of (Formula presented.).

KW - Average distance

KW - Mellin transform

KW - Moments

KW - Self-similar measures

KW - Self-similar set

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

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Keywords

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