关于势函数与黎曼流形的准等谱性
On quasi-isospectrality of potentials and Riemannian manifolds
AI总结：
本文研究了准等谱算子的性质，证明了奇数维闭合流形的准等谱性实际上等价于等谱性，并扩展了紧致性结果。
摘要：
本文研究准等谱算子作为等谱算子的推广。文章包含综述性内容和原创结果。我们首先回顾已知的紧致流形和有限区间上等谱势函数的结果，然后引入准等谱性的概念。接着，我们研究BMT方法作为系统构造有限区间上准等谱Sturm-Liouville算子的系统方法，并将其应用于多个边界值问题。我们的主要结果表明，任何两个准等谱的闭合奇数维流形实际上都是等谱的。此外，我们通过热追踪渐进行为将经典紧致流形上等谱势函数的紧致性结果扩展到准等谱设置中。
英文摘要：
In this article, we study quasi-isospectral operators as a generalization of isospectral operators. The paper contains both expository material and original results. We begin by reviewing known results on isospectral potentials on compact manifolds and finite intervals, and then introduce the notion of quasi-isospectrality. We next investigate the BMT method as a systematic approach to constructing quasi-isospectral Sturm-Liouville operators on a finite interval, and apply it to several boundary value problems. Our main result shows that any two quasi-isospectral closed manifolds of odd dimension are, in fact, isospectral. In addition, we extend classical compactness results for isospectral potentials on low-dimensional manifolds to the quasi-isospectral setting via heat trace asymptotics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
