Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectra
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- by Jonathan Eckhardt and Gerald Teschl PDF
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Abstract:
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 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.References
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Additional Information
- Jonathan Eckhardt
- Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria
- MR Author ID: 951030
- ORCID: 0000-0001-6902-0606
- Email: jonathan.eckhardt@univie.ac.at
- Gerald Teschl
- Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria — and — International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
- Email: Gerald.Teschl@univie.ac.at
- Received by editor(s): October 11, 2011
- Received by editor(s) in revised form: February 28, 2012
- Published electronically: November 27, 2012
- Additional Notes: This research was supported by the Austrian Science Fund (FWF) under Grant No. Y330
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3923-3942
- MSC (2010): Primary 34B20, 34L05; Secondary 34B24, 47A10
- DOI: https://doi.org/10.1090/S0002-9947-2012-05821-1
- MathSciNet review: 3042609