论文标题
关于准同色潜力
On quasi-isospectral potentials
论文作者
论文摘要
在本文中，我们将与准同性操作员合作，作为同一操作员的概括。首先，我们回顾一些有关紧凑型歧管和有限间隔的等光势的已知结果。然后，我们考虑了准次谱的概念，并推断出准染色电位的几种特性。接下来，我们研究BMT方法是一种系统的方法，用于在有限的间隔内构建准柔性sturm-liouville操作员。它在各种边界价值问题上的应用可说明该方法的独特特征及其局限性。最后，我们使用热量迹线扩展了在低维的流形上，将等光势的经典紧凑型结果扩展到准膜片电位。
In this article, we work with quasi-isospectral operators as a generalization of isospectral operators. We begin by reviewing some known results about isospectral potentials on compact manifolds and finite intervals. We then consider the notion of quasi-isospectrality, and deduce several properties of quasi-isospectral potentials. Next, we investigate the BMT method as a systematic approach for constructing quasi-isospectral Sturm-Liouville operators on a finite interval. Its application to various boundary value problems serves to illustrate both the method's distinctive features and its limitations. Finally, we extend classical compactness results of isospectral potentials on manifolds of low dimensions to quasi-isospectral potentials using the heat trace.
