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Scattering theory for Riemannian Laplacians
http://hdl.handle.net/2241/119198
http://hdl.handle.net/2241/1191981e179b1a-e71d-4676-b185-00b8a1c214ae
名前 / ファイル | ライセンス | アクション |
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JFA_264-8.pdf (314.7 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2013-05-22 | |||||
タイトル | ||||||
タイトル | Scattering theory for Riemannian Laplacians | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Ito, K.
× Ito, K.× Skibsted, E. |
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著者別名 |
伊藤, 健一
× 伊藤, 健一 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We introduce a notion of scattering theory for the Laplace–Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behavior of the metric at infinity (like asymptotic Euclidean or hyperbolic metrics studied previously in the literature). A consequence of the theory is spectral theory for the Laplace–Beltrami operator including identification of the continuous spectrum and absence of singular continuous spectrum. | |||||
書誌情報 |
Journal of functional analysis 巻 264, 号 8, p. 1929-1974, 発行日 2013-04 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0022-1236 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00252370 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1016/j.jfa.2013.02.002 | |||||
権利 | ||||||
権利情報 | © 2013 Elsevier Inc. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of functional analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of functional analysis, VOL.264, ISSUE.8, 2013 DOI:10.1016/j.jfa.2013.02.002 | |||||
著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Elsevier Inc. | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2241/119198 | |||||
識別子タイプ | HDL |