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The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition. / Chelkak, Dmitry; Korotyaev, Evgeny.

In: Annales Henri Poincare, Vol. 8, No. 6, 09.2007, p. 1115-1150.

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

Harvard

Chelkak, D & Korotyaev, E 2007, 'The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition', Annales Henri Poincare, vol. 8, no. 6, pp. 1115-1150. https://doi.org/10.1007/s00023-007-0330-z

APA

Chelkak, D., & Korotyaev, E. (2007). The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition. Annales Henri Poincare, 8(6), 1115-1150. https://doi.org/10.1007/s00023-007-0330-z

Vancouver

Chelkak D, Korotyaev E. The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition. Annales Henri Poincare. 2007 Sep;8(6):1115-1150. https://doi.org/10.1007/s00023-007-0330-z

Author

Chelkak, Dmitry ; Korotyaev, Evgeny. / The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition. In: Annales Henri Poincare. 2007 ; Vol. 8, No. 6. pp. 1115-1150.

BibTeX

@article{a87b4935d5ff41b8a730c5abb76e1ed5,
title = "The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition",
abstract = "We consider the perturbed harmonic oscillator TDψ = -ψ″ + x2 ψ + q(x)ψ, ψ(0)=0, in L2 (ℝ+), where q ∈ H+ = {q′, xq ∈ L 2 (ℝ+)} is a real-valued potential. We prove that the mapping q & spectral data = {eigenvalues of T D} ⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q ∈ H+ is given.",
author = "Dmitry Chelkak and Evgeny Korotyaev",
note = "Funding Information: Evgeny Korotyaev was partly supported by DFG project BR691/23-1. Some part of this paper was written at the Mittag–Leffler Institute, Stockholm. The authors are grateful to the Institute for the hospitality.",
year = "2007",
month = sep,
doi = "10.1007/s00023-007-0330-z",
language = "English",
volume = "8",
pages = "1115--1150",
journal = "Annales Henri Poincare",
issn = "0018-0238",
publisher = "Birkh{\"a}user Verlag AG",
number = "6",

}

RIS

TY - JOUR

T1 - The inverse problem for perturbed harmonic oscillator on the half-line with a Dirichlet boundary condition

AU - Chelkak, Dmitry

AU - Korotyaev, Evgeny

N1 - Funding Information: Evgeny Korotyaev was partly supported by DFG project BR691/23-1. Some part of this paper was written at the Mittag–Leffler Institute, Stockholm. The authors are grateful to the Institute for the hospitality.

PY - 2007/9

Y1 - 2007/9

N2 - We consider the perturbed harmonic oscillator TDψ = -ψ″ + x2 ψ + q(x)ψ, ψ(0)=0, in L2 (ℝ+), where q ∈ H+ = {q′, xq ∈ L 2 (ℝ+)} is a real-valued potential. We prove that the mapping q & spectral data = {eigenvalues of T D} ⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q ∈ H+ is given.

AB - We consider the perturbed harmonic oscillator TDψ = -ψ″ + x2 ψ + q(x)ψ, ψ(0)=0, in L2 (ℝ+), where q ∈ H+ = {q′, xq ∈ L 2 (ℝ+)} is a real-valued potential. We prove that the mapping q & spectral data = {eigenvalues of T D} ⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q ∈ H+ is given.

UR - http://www.scopus.com/inward/record.url?scp=35148826413&partnerID=8YFLogxK

U2 - 10.1007/s00023-007-0330-z

DO - 10.1007/s00023-007-0330-z

M3 - Article

AN - SCOPUS:35148826413

VL - 8

SP - 1115

EP - 1150

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 0018-0238

IS - 6

ER -

ID: 86256368