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Radiation condition bounds on manifolds with ends

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Radiation condition bounds on manifolds with ends. / Ito, K.; Skibsted, E.
In: Journal of Functional Analysis, Vol. 278, No. 9, 108449, 15.05.2020.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Ito, K & Skibsted, E 2020, 'Radiation condition bounds on manifolds with ends', Journal of Functional Analysis, vol. 278, no. 9, 108449. https://doi.org/10.1016/j.jfa.2019.108449

APA

Ito, K., & Skibsted, E. (2020). Radiation condition bounds on manifolds with ends. Journal of Functional Analysis, 278(9), [108449]. https://doi.org/10.1016/j.jfa.2019.108449

CBE

Ito K, Skibsted E. 2020. Radiation condition bounds on manifolds with ends. Journal of Functional Analysis. 278(9):Article 108449. https://doi.org/10.1016/j.jfa.2019.108449

MLA

Ito, K. and E. Skibsted. "Radiation condition bounds on manifolds with ends". Journal of Functional Analysis. 2020. 278(9). https://doi.org/10.1016/j.jfa.2019.108449

Vancouver

Ito K, Skibsted E. Radiation condition bounds on manifolds with ends. Journal of Functional Analysis. 2020 May 15;278(9):108449. doi: 10.1016/j.jfa.2019.108449

Author

Ito, K. ; Skibsted, E. / Radiation condition bounds on manifolds with ends. In: Journal of Functional Analysis. 2020 ; Vol. 278, No. 9.

Bibtex

@article{c2aee7029d70438f9b552ec95484833f,
title = "Radiation condition bounds on manifolds with ends",
abstract = "We study spectral theory for the Schr{\"o}dinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Certain exterior domains for possibly unbounded obstacles are included. We prove Rellich's theorem, the limiting absorption principle, radiation condition bounds and the Sommerfeld uniqueness result, striving to extending and refining previously known spectral results on manifolds. The proofs are given by an extensive use of commutator arguments. These arguments have a classical spirit (essentially) not involving energy cutoffs or microlocal analysis and require, presumably, minimum regularity and decay properties of perturbations. This paper has interest of its own right, but it also serves as a basis for the stationary scattering theory developed fully in the sequel [19].",
keywords = "Commutator argument, Riemannian manifold, Schr{\"o}dinger operator, Spectral theory",
author = "K. Ito and E. Skibsted",
year = "2020",
month = may,
day = "15",
doi = "10.1016/j.jfa.2019.108449",
language = "English",
volume = "278",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "9",

}

RIS

TY - JOUR

T1 - Radiation condition bounds on manifolds with ends

AU - Ito, K.

AU - Skibsted, E.

PY - 2020/5/15

Y1 - 2020/5/15

N2 - We study spectral theory for the Schrödinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Certain exterior domains for possibly unbounded obstacles are included. We prove Rellich's theorem, the limiting absorption principle, radiation condition bounds and the Sommerfeld uniqueness result, striving to extending and refining previously known spectral results on manifolds. The proofs are given by an extensive use of commutator arguments. These arguments have a classical spirit (essentially) not involving energy cutoffs or microlocal analysis and require, presumably, minimum regularity and decay properties of perturbations. This paper has interest of its own right, but it also serves as a basis for the stationary scattering theory developed fully in the sequel [19].

AB - We study spectral theory for the Schrödinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Certain exterior domains for possibly unbounded obstacles are included. We prove Rellich's theorem, the limiting absorption principle, radiation condition bounds and the Sommerfeld uniqueness result, striving to extending and refining previously known spectral results on manifolds. The proofs are given by an extensive use of commutator arguments. These arguments have a classical spirit (essentially) not involving energy cutoffs or microlocal analysis and require, presumably, minimum regularity and decay properties of perturbations. This paper has interest of its own right, but it also serves as a basis for the stationary scattering theory developed fully in the sequel [19].

KW - Commutator argument

KW - Riemannian manifold

KW - Schrödinger operator

KW - Spectral theory

UR - http://www.scopus.com/inward/record.url?scp=85077715329&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2019.108449

DO - 10.1016/j.jfa.2019.108449

M3 - Journal article

AN - SCOPUS:85077715329

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 9

M1 - 108449

ER -