Gesztesy, Fritz and Simon, Barry (2000) Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum. Transactions of the American Mathematical Society, 352 (6). pp. 2765-2787. ISSN 0002-9947. doi:10.1090/S0002-9947-99-02544-1. https://resolver.caltech.edu/CaltechAUTHORS:20180511-153128441
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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 = -(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.
| Item Type: | Article | |||||||||
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| Additional Information: | © Copyright 2000 by the Authors. Received by the editors October 9, 1997. This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491. | |||||||||
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| Issue or Number: | 6 | |||||||||
| Classification Code: | 2000 Mathematics Subject Classification. Primary 34A55, 34L40; Secondary 34B20. | |||||||||
| DOI: | 10.1090/S0002-9947-99-02544-1 | |||||||||
| Record Number: | CaltechAUTHORS:20180511-153128441 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180511-153128441 | |||||||||
| Official Citation: | Gesztesy, F., & Simon, B. (2000). Inverse Spectral Analysis with Partial Information on the Potential, II. The Case of Discrete Spectrum. Transactions of the American Mathematical Society, 352(6), 2765-2787. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 86374 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 11 May 2018 22:36 | |||||||||
| Last Modified: | 15 Nov 2021 20:38 |
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