Speaker: Kunyu Guo (Fudan University)
Abstract: This talk concerns a long-standing problem raised by Beurling and Wintner on completeness of the dilation system generated by the odd periodic functions on the real numbers. Up to now there has been no explicit description of solutions of the Beurling-Wintner problem, even for characteristic functions. Focusing on the union of finitely many intervals with rational endpoints and using substantially techniques from analytic number theory, we fully solved the Beurling-Wintner problem in most interesting situations and exhibit the explicit form of such sets. As a consequence, it yields a complete solutions for the rational version of Kozlov’s problem. Moreover, we find that the rational version of Kozlov’s problem is closely related to the Twin Prime Problem and the Sophie Germain Prime Problem.
Time: 2025-09-26 14:30:00
Location: R1410, SIMIS
Introduction to the speaker: Kunyu Guo is a Distinguished Professor at Fudan University and a Tenured Professor at the Gu Institute (谷超豪研究所), Shanghai Mathematical Center. His research primarily focuses on functional analysis and operator theory. He has twice been awarded the first prize of the Shanghai Natural Science Award (as the first completer both times). He has long been engaged in teaching and research in functional analysis and operator theory , having published over 100 papers in functional analysis and operator theory and authored three monographs.
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