Article
Trans. Amer. Math. Soc. (to appear)
Uniqueness Results for One-Dimensional Schrödinger Operators with Purely Discrete Spectra
Jonathan Eckhardt and Gerald Teschl
We provide an abstract framework for singular one-dimensional Schrödinger operators with purely discrete spectra
to show when the spectrum plus norming constants determine such an operator completely. As an example we apply
our findings to prove a new uniqueness results for perturbed quantum mechanical harmonic oscillators. In addition, we
also show how to establish a Hochstadt-Lieberman type result for these operators. Our approach is based on
the singular Weyl-Titchmarsh-Kodaira theory which is extended to cover the present situation.
MSC2010: Primary 34B20, 34L05; Secondary 34B24, 47A10
Keywords: Schrödinger operators, inverse spectral theory, discrete spectra
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