Uniqueness theorems for Sturm-Liouville operators with interior twin-dense nodal set

Abstract

We study Inverse problems for the Sturm-Liouville operator with Robin boundary conditions. We establish two uniqueness theorems from the twin-dense nodal subset $W_{S}([\frac{1-\varepsilon}{2},\frac{1}{2}])$, $ 0<\varepsilon\leq1$, together with parts of either one spectrum, or the minimal nodal subset $\{x_n^1\}_{n=1}^\infty$ on the interval [0,1/2]. In particular, if one spectrum is given a priori, then the potential q on the whole interval [0,1] can be uniquely determined by $W_{S}([\frac{1-\varepsilon}{2},\frac{1}{2}])$ for any S and arbitrarily small $\varepsilon$.

Keywords

• Uniqueness theorem
• inverse nodal problem
• potential
• Sturm-Liouville operator
• the interior twin-dense nodal subset