On quasi-isospectral potentials

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.