## Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum

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- by Fritz Gesztesy and Barry Simon PDF
- Trans. Amer. Math. Soc.
**352**(2000), 2765-2787

## Abstract:

We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential $q$ of a one-dimensional Schrödinger operator $H=-\frac {d^{2}}{dx^{2}}+q$ determine the potential completely. Included are theorems for finite intervals and for the whole line. In particular, we pose and solve a new type of inverse spectral problem involving fractions of the eigenvalues of $H$ on a finite interval and knowledge of $q$ over a corresponding fraction of the interval. The methods employed rest on Weyl $m$-function techniques and densities of zeros of a class of entire functions.## References

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## Additional Information

**Fritz Gesztesy**- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 72880
- Email: fritz@math.missouri.edu
**Barry Simon**- Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 189013
- Email: bsimon@caltech.edu
- Received by editor(s): October 9, 1997
- Published electronically: December 10, 1999
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.
- © Copyright 2000 by the Authors
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 2765-2787 - MSC (2000): Primary 34A55, 34L40; Secondary 34B20
- DOI: https://doi.org/10.1090/S0002-9947-99-02544-1
- MathSciNet review: 1694291