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math.CA2018
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…
math.CA2018
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…