Amir Algom: Fourier decay for self-conformal measures

Abstract:  A self-conformal measure is a measure P that is invariant, in some sense, under a finite set of smooth contractions of an interval. Introducing a new method, we prove that the Fourier transform of P decays to zero at infinity and give quantitative estimates on the rate of decay, under mild and natural conditions. This complements the highly active study of Fourier decay for dynamically defined measures, dating back to the important work of Erdos about Bernoulli convolutions.

Joint work with Federico Rodriguez Hertz and Zhiren Wang.