Fourier decay of self-similar measures on the complex plane

CAROLINA MOSQUERA, ANDREA OLIVO

Journal of Fractal Geometry

European Mathematical Society Press

Lugar: Zurich; Año: 2022

2308-1309

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, first by R. Kaufman, and later, with quantitative bounds, by the first author and P. Shmerkin. Also we derive several applications concerning correlation dimension and Frostman exponent of these measures. Furthermore, we present a generalization for a particular case on R^n, with n≥3.