275 citations · 1k across the 37 of their papers we have counts for
41 papers
Realizing trees of configurations in thin sets
Allan Greenleaf, Alex Iosevich, Krystal Taylor
Let be a continuous function, smooth away from the diagonal, such that, for some , the associated generalized Radon transforms \begin{equation} \label{Radon} R_t^ϕf(x…
On restricted Falconer distance sets
José Gaitan, Allan Greenleaf, Eyvindur Ari Palsson +1
We introduce a class of Falconer distance problems, which we call of restricted type, lying between the classical version and its pinned variant. Prototypical restricted distance s…
Nonempty interior of configuration sets via microlocal partition optimization
Allan Greenleaf, Alex Iosevich, Krystal Taylor
We prove new results of Mattila-Sjölin type, giving lower bounds on Hausdorff dimensions of thin sets ensuring that various -point configuration sets, genera…
Microlocal analysis of borehole seismic data
Raluca Felea, Romina Gaburro, Allan Greenleaf +1
Borehole seismic data is obtained by receivers located in a well, with sources located on the surface or in another well. Using microlocal analysis, we study possible approximate r…
On -point configuration sets with nonempty interior
Allan Greenleaf, Alex Iosevich, Krystal Taylor
We give conditions for -point configuration sets of thin sets to have nonempty interior, applicable to a wide variety of configurations. This is a continuation of our earlier wo…
Configuration sets with nonempty interior
Allan Greenleaf, Alex Iosevich, Krystal Taylor
A theorem of Steinhaus states that if has positive Lebesgue measure, then the difference set contains a neighborhood of . Similarly, if merely h…