The high-order estimate of the entire function associated with inverse Sturm–Liouville problems

Abstract

The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math. Phys. 50 2009, 3, Article ID 033505] remains true for more general case.