40 citations · 176 across the 31 of their papers we have counts for
7 papers · 1 filter
Intersections of thick compact sets in
Kenneth Falconer, Alexia Yavicoli
We introduce a definition of thickness in and obtain a lower bound for the Hausdorff dimension of the intersection of finitely or countably many thick compact sets u…
The fractal structure of elliptical polynomial spirals
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensi…
The density of sets containing large similar copies of finite sets
Kenneth Falconer, Vjekoslav Kovač, Alexia Yavicoli
We prove that if () is a Lebesgue-measurable set with density larger than , then contains similar copies of every -point…
Minkowski dimension for measures
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literatur…
Projection theorems for intermediate dimensions
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions m…
A Hölder-type inequality on a regular rooted tree
Kenneth J Falconer
We establish an inequality which involves a non-negative function defined on the vertices of a finite -ary regular rooted tree. The inequality may be thought of as relating an i…