Partial Information for Inverse Spectral Uniqueness in Vibration System with Multiple Frozen Arguments

Lung-Hui Chen

paper

Partial Information for Inverse Spectral Uniqueness in Vibration System with Multiple Frozen Arguments

arXiv:2507.20184

Abstract

In this paper, we investigate the inverse spectral problem of the Sturm-Liouville operator with many frozen arguments fixed at the points ${a_{1}, a_{2}, \dots, a_{N}}$ in $(0, I ¨ )$ . We start with counting the zeros or the eigenvalues of characteristic function, and then discuss how certain information provided a priori on the point set ${a_{1}, a_{2}, \dots, a_{N}}$ would affect the uniqueness or non-uniqueness of this vibration system with many frozen points. The knowledge at the frozen or regulator points are practical in many on-site problems. Parallelly, certain irrational independence assumption assures the inverse spectral uniqueness as well.