92 citations · 502 across the 56 of their papers we have counts for
20 papers · 1 filter
On the dimension of orthogonal projections of self-similar measures
Amir Algom, Pablo Shmerkin
Let be a self similar measure on , , and let be an orthogonal projection onto a -dimensional subspace. We formulate a criterion on the action of t…
On normal numbers and self-similar measures
Amir Algom, Simon Baker, Pablo Shmerkin
Let be a self-similar IFS on and let be a Pisot number. We prove that if fo…
dimensions of self-similar measures, and applications: a survey
Pablo Shmerkin
We present a self-contained proof of a formula for the dimensions of self-similar measures on the real line under exponential separation (up to the proof of an inverse theore…
Absolute continuity of non-homogeneous self-similar measures
Santiago Saglietti, Pablo Shmerkin, Boris Solomyak
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M.…
On Furstenberg's intersection conjecture, self-similar measures, and the norms of convolutions
Pablo Shmerkin
We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measure…
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
Ian D. Morris, Pablo Shmerkin
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-…