Joint BCAM-UPV/EHU Analysis and PDE seminar: Some problems related to the Fourier decay of homogeneous self-similar measures

In this seminar, we are going to talk about the behavior of homogeneous self-similar measures and their Fourier transform. It is known that, in some cases, the Fourier transform of a self-similar measure does not go to zero as the frequencies go to infinity; nevertheless, it can have power decay outside of a sparse set of frequencies. We will go over this result and show some consequences of it. Additionally, we will discuss about the $L^p$ improvement property of such measures as part of an ongoing project.