走向现代数学学术报告 - 郭坤宇教授（No. 703）

报告题目：The Beurling-Kozlov-Wintner completeness problem

报告人：郭坤宇 教授（复旦大学）

报告时间：2024年5月10日 14:00

报告地点：东海岸校区-D实209

报告摘要：This talk concerns a long-standing problem on completeness of function systems generated by odd periodic extensions of functions in L^2(0,1). This problem, raised by Beurling and Wintner in the 1940s, is closely related to the Riemann Hypothesis. The Beurling-Wintner problem is also known as the Periodic Dilation Completeness Problem. As far as we know, there is still no specific criteria that can be directly used to check if the p.d.s of a function $\varphi$ is complete, even in the simplest case where $\varphi$ is a characteristic function, as first considered by Kozlov in 1950--the Kozlov completeness problem. We completely solve the rational version of step functions (that is, those functions with rational jump discontinuities) by approaches from analytic number theory, and present several deep applications including a complete solution to the rational version of Kozlov completeness problem. This is a joint work with Dr. Hui Dan.

报告人简介：郭坤宇，复旦大学数学科学学院教授, 博士生导师。2005年获国家杰出青年科学基金。曾任复旦大学数学科学学院院长、非线性数学模型与方法教育部重点实验室主任，现为第十四届全国政协委员。长期从事基础数学的教学和科研工作，在国际知名数学期刊发表论文 90多篇: 其中包括JFA(13篇)、Crelle’s Journal（3篇)、Adv. in Math. (2篇) 等; 国外出版专著2部(Lecture Notes in Math； π-Research Notes in Math.)。发展的思想、方法被学界同行称为 “郭方法”； “郭引理”；“郭-稳定性”； “郭-王定理”；“郭-王恒等式”等。 解决了算子理论中多个困难的问题，形成了复旦大学算子理论研究特色，国际同行称为“复旦学派”。