This note demonstrates that knowing a few spectra can entirely determine the potential in one-dimensional Schrödinger operators, suggesting new approaches for analysis.
The [Horváth, Tran. Amer. Math. Soc. 353, 4155–4171, (2001)] proves that, under certain conditions, knowledge of finitely many spectra and partial information about the potential entirely determine the potential. In this note, we generalize the this result to the case where the potential function is sufficiently smooth at the right endpoint a(∈ (0, 1)).
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Tiezheng Li (2025) studied this question.
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