5 papers · 1 filter
The Entropy of Cantor--like measures
Kathryn E. Hare, Kevin G. Hare, Brian P. M. Morris +1
By a Cantor-like measure we mean the unique self-similar probability measure satisfying where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdo…
Sidon sets are proportionally Sidon with small Sidon constants
Kathryn E. Hare, Robert, Yang
In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was sho…
Local dimensions of overlapping self-similar measures
Kathryn E. Hare, Kevin G. Hare
We show that any equicontractive, self-similar measure arising from the IFS of contractions , with self-similar set , admits an isolated point in its set of local d…
Quasi-doubling of self-similar measures with overlaps
Kathryn Hare, Kevin Hare, Sascha Troscheit
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure the…
The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra
Jonathan M. Fraser, Kathryn E. Hare, Kevin G. Hare +2
We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the `upper Assouad spectrum'. These spectra are designed to interpolate bet…