An \(n\)-dimensional Borg--Levinson theorem for singular potentials
type: Item
instance of: scholarly article
title: An \(n\)-dimensional Borg--Levinson theorem for singular potentials
zbMATH Open document ID: 1028.35170
DOI: 10.1016/S0196-8858(02)00027-1
author: Lassi Päivärinta
author: Valery Serov
published in: Advances in Applied Mathematics
publication date: 2003-04-02T00:00:00Z
review text: It is proved that the boundary spectral data, i.e. the Dirichlet eigenvalues and normal derivatives of the eigenfunctions at the boundary, determines uniquely the potential \(q\) in \(L^p\) for the Schrödinger equation \((-\Delta+ q)u= 0\) in a bounded domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 2\), \(p> n/2\). This result generalizes the result of Nachman, Sylvester and Uhlmann to unbounded potentials and it can be viewed as an \(n\)-dimensional Borg-Levinson theorem.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 1891076
zbMATH Keywords: inverse spectral problem
zbMATH Keywords: uniqueness
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: unbounded potentials
zbMATH Keywords: Borg-Levinson theorem
reviewed by: Daniel Lesnic
MaRDI profile type: Publication
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full work available at URL: s0196-8858(02)00027-1
OpenAlex ID: W2080226427
description: scientific article; zbMATH DE number 1891076