Joint BCAM-UPV/EHU Analysis and PDE seminar: Fourier decay of self-similar measures on the complex plane

LOCATION: UPV/EHU room to be announced

Abstract
We prove that the Fourier transform of self-similar measures on the complex plane has fast decay outside of a very sparse set of frequencies, with quantitative estimates, extending the results obtained in the real line by R. Kaufman. Also we derive several applications concerning correlation dimension and Frostman exponent of complex Bernoulli convolutions. Furthermore, we present a generalisation for a particular case on Rd, with d ≥ 3.

The results are based on a joint work with Andrea Olivo.

More info at https://sites.google.com/view/apdebilbao/home