Sturm-Liouville problem with general inverse symmetric potential
Keywords:
boundary conditions, the inverse eigenvalue problem, general inverse Sturm-Liouville, problem symmetric potentialAbstract
For an inverse nonselfadjoint Sturm-Liouville problem with a symmetric potential and general boundary conditions, the uniqueness theorems are established and proven. Six eigenvalues and a spectrum are the spectral information utilized for the original reconstruction of Sturm-Liouville problems. Additionally, it is established that an inverse self-adjoint Sturm-Liouville problem with symmetric potential and nonseparated boundary conditions is unique. The unique reconstruction of Sturm-Liouville problems is accomplished by these theorems using a spectrum and two (or three) eigenvalues. The theorems apply the traditional Sturm-Liouville results of G. Borg and N. Levinson to the case of problems with general boundary conditions. With symmetric potential and general boundary conditions, schemes for the original reconstruction of Sturm-Liouville problems are provided.
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