On the Fourier decay for self-similar measures

A finite positive measure on the Euclidean space is called Rajchman if its Fourier transform tends to zero at infinity. 

Absolutely continuous measures are Rajchman by the Riemann-Lebesgue Lemma, but it is a delicate question to decide which singular measures are such. 

For many purposes simple convergence if the Fourier transform to zero is not sufficient and some quantitative decay is needed. 

Recently there has been renewed interest and a lot of activity in studying such questions for ``fractaI'' measures. 

I will survey results on Fourier decay for some classes of fractal measures, such as the ``natural'' uniform measure on a Cantor set of a uniform contraction ratio and their generalizations. 

Some of these results are classical, going back to Erdos, Salem, and Kahane, and some are recent.