4 papers · 2 filters
New results on embeddings of self-similar sets via renormalization
Amir Algom, Michael Hochman, Meng Wu
For self-similar sets , we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conj…
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…
Polynomial Fourier decay and a cocycle version of Dolgopyat's method for self conformal measures
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
We show that every self conformal measure with respect to a IFS has polynomial Fourier decay under some mild and natural non-linearity conditions. In partic…
Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture
Amir Algom, Zhiren Wang
In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system , $\frac{1}{\log N} \sum_{n=1} ^N \…