发表机构
CNRS; Laboratoire Jacques-Louis Lions, LJLL（法国国家科学研究中心; 雅克-路易·利翁斯实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文系统研究了概周期函数的均匀振荡长度，证明了零均值标量概周期函数存在均匀振荡长度，并探讨了连续介质力学中相关函数的振荡上界，最后回顾了方形薄膜振动的未解问题。
AI 中文摘要
本文对文献中从未以这种形式呈现过的分散结果提供了一个综合视角。首先，我们精确研究了周期函数的振荡长度。然后，我们证明了任何具有零均值的标量概周期函数都存在一个均匀振荡长度。之后，我们研究了连续介质力学研究中出现的一些概周期函数的振荡长度的上界，并证明了在某些振动连续介质的任何开子集中，关于时间存在有限的振荡长度。论文最后回顾了一个关于固定边界方形薄膜振动的长期未解问题。
英文摘要
A synthetic view is provided on scattered results which were never presented in this form in the literature. First we investigate precisely the oscillation length for periodic functions. Then, we establish the existence of a uniform oscillation lentgh for any scalar almost periodic function with mean-value 0. After that, we investigate upper bounds of the oscillation length for some almost periodic functions which appear in the study of continuum mechanics, and we show the existence of a finite oscillation length with respect to time in any open subset of some vibrating continuous media. The paper finally recalls a long standing open problem on the vibrations of a square membrane with fixed edge.
