杏吧传媒 数学大讲坛第三期

第二十六讲——奥卢大学吴猛研究员学术报告II

题目：On Fourier transforms of self-similar measures

时间：2023年5月10日（周三）19：00-20：00

地点：腾讯会议（会议ID：817-1466-5240）

报告人：吴猛研究员

摘要:In this series of lectures, we shall talk about Fourier tranforms of self-similar measures and their non-linear images. We shall in particular focus on a result of R.Kaufman which states that all C^2 non-linear images of Bernoulli convolutions have power Fourier decays. During the courses, basic notions on self-similar measures will be recalled, some useful techniques for studying fractal dimensions and Fourier transforms of these measures will be introduced.

（1）In the first lecture, we shall review some classical facts about fractal measures and introduce measures with non-Fourier decay, uniqueness sets, Salem measures and sets, ...

（2）In the second and third lectures, we shall see that having non-Fourier decay is atypical in the world of self-similar measures. We shall also see that if we perturbate a self-similar measure by a non-linear transform, then the image measure will have polynomial Fourier decay. We shall present the detailed proof of this beautiful result of Kaufman. If time permits, we shall also mention some recent related results on Fourier decay of self-similar or self-conformal measures.

报告人简介：

吴猛，奥卢大学（芬兰）研究员。2013年于亚眠大学（法国）获得博士学位。主要研究方向为动力系统和分形几何及其在数论等领域的应用。研究成果已在Ann. Math., Adv. Math. ,Int. Math. Res. Not., Israel. J. Math.，Math. Z.等数学期刊上发表。