报告人:章逸平 教授（武汉大学）

报告题目：LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS

报告摘要：The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.

报告时间: 2017年6月9日上午10:00-11:00

报告地点: 科技楼南楼702室