An n-dimensional Borg-Levinson theorem

Adrian Nachman; John Sylvester; Gunther Uhlmann

doi:10.1007/BF01224129

An n-dimensional Borg-Levinson theorem

Adrian Nachman^*, John Sylvester, Gunther Uhlmann

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

169 Citations (Scopus)

Abstract

We show that the potential q is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator -Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝⁿ. This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.

Original language	English
Pages (from-to)	595-605
Number of pages	11
Journal	Communications in Mathematical Physics
Volume	115
Issue number	4
DOIs	https://doi.org/10.1007/BF01224129
Publication status	Published - Dec 1988
Externally published	Yes

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title = "An n-dimensional Borg-Levinson theorem",

abstract = "We show that the potential q is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schr{\"o}dinger operator -Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝn. This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.",

author = "Adrian Nachman and John Sylvester and Gunther Uhlmann",

year = "1988",

month = dec,

doi = "10.1007/BF01224129",

language = "English",

volume = "115",

pages = "595--605",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

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T1 - An n-dimensional Borg-Levinson theorem

AU - Nachman, Adrian

AU - Sylvester, John

AU - Uhlmann, Gunther

PY - 1988/12

Y1 - 1988/12

N2 - We show that the potential q is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator -Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝn. This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.

AB - We show that the potential q is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator -Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝn. This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:A1988M666700004

UR - https://openalex.org/W2058356772

UR - https://www.scopus.com/pages/publications/0000636457

U2 - 10.1007/BF01224129

DO - 10.1007/BF01224129

M3 - Journal Article

SN - 0010-3616

VL - 115

SP - 595

EP - 605

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 4

ER -

An n-dimensional Borg-Levinson theorem

Abstract

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