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

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.

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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.

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Simon, Barry0000-0003-2561-8539
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.
Funding AgencyGrant Number
Issue or Number:6
Classification Code:2000 Mathematics Subject Classification. Primary 34A55, 34L40; Secondary 34B20.
Record Number:CaltechAUTHORS:20180511-153128441
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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
Deposited By: George Porter
Deposited On:11 May 2018 22:36
Last Modified:15 Nov 2021 20:38

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