Radiation condition bounds on manifolds with ends

K. Ito; E. Skibsted

doi:10.1016/j.jfa.2019.108449

Radiation condition bounds on manifolds with ends

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

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].

Originalsprog	Engelsk
Artikelnummer	108449
Tidsskrift	Journal of Functional Analysis
Vol/bind	278
Nummer	9
ISSN	0022-1236
DOI	https://doi.org/10.1016/j.jfa.2019.108449
Status	Udgivet - 15 maj 2020

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AU - Skibsted, E.

PY - 2020/5/15

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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

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KW - Spectral theory

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DO - 10.1016/j.jfa.2019.108449

M3 - Journal article

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SN - 0022-1236

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

Radiation condition bounds on manifolds with ends

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