报告题目:  Loomis Type Theorem on Half-line

报告人: 简伟刚 博士 (豫章师范学院)

时间: 2024年8月5日 (周一) 10:00-11:00

地点: 理科楼A304

摘要: In this talk，we present a Loomis type theorem on the half-line. In the 1960s, Loomis published his famous theorem: a bounded and uniformly continuous function defined on $ \mathbb{R} $ is almost periodic when its spectrum is at most countable. However, a bounded and uniformly continuous function defined on $ \mathbb{R}^{+} $ is  not necessary asymptotically almost periodic even if the spectrum is a single point set. By establishing a Kadets type theorem for asymptotically almost periodic functions, we obtain our Loomis type theorem: discreteness of spectrum of bounded and uniformly continuous functions defined on $\mathbb{R}^{+} $ implies remotely almost periodicity (weaker than asymptotically almost periodicity). The Loomis type theorem in this paper removed the ergodicity assumption in the results of Batty et al., and is a natural extension on $\mathbb{R}^{+} $ of the classical Loomis theorem. This is joint work with Ding Hui-Sheng.

邀请人: 步尚全