6 papers · 1 filter
A non-abelian, non-Sidon, completely bounded set
Kathryn Hare, Parasar Mohanty
The purpose of this note is to construct an example of a discrete non-abelian group and a subset of , not contained in any abelian subgroup, that is a completely bounded…
The -spectrum for a class of self-similar measures with overlap
Kathryn E. Hare, Kevin G. Hare, Wanchun Shen
It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the -fold convolution of the C…
Measures with specified support and arbitrary Assouad dimensions
Kathryn E. Hare, Franklin Mendivil, Leandro Zuberman
We show that if the upper Assouad dimension of the compact set is positive, then given any there is a measure with support and upper Assou…
The smoothness of convolutions of orbital measures on complex Grassmannian symmetric spaces
Sanjiv Kumar Gupta, Kathryn E. Hare
It is well known that if is any irreducible symmetric space and is a continuous orbital measure supported on the double coset then the convolution product, $μ_…
Almost sure Assouad-like Dimensions of Complementary sets
Ignacio García, Kathryn E. Hare, Franklin Mendivil
Given a non-negative, decreasing sequence with sum , we consider all the closed subsets of such that the lengths of their complementary open intervals are given by t…
Intermediate Assouad-like dimensions
Ignacio García, Kathryn Hare, Franklin Mendivil
We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and -spectrum are other special examples…