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上半空間での正値調和関数について
https://shotoku.repo.nii.ac.jp/records/1686
https://shotoku.repo.nii.ac.jp/records/1686471efbd5-4066-4f1d-b91e-452c14d4bdcb
名前 / ファイル | ライセンス | アクション |
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KJ00000110371.pdf (277.8 kB)
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Item type | [ELS]紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2017-03-17 | |||||
タイトル | ||||||
タイトル | 上半空間での正値調和関数について | |||||
タイトル | ||||||
タイトル | On positive harmonic functions in the upper half space | |||||
言語 | ||||||
言語 | jpn | |||||
キーワード | ||||||
主題 | Kelvin transformation | |||||
資源タイプ | ||||||
著者 |
加藤, 政壽美
× 加藤, 政壽美× Kato, Masasumi |
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抄録(英) | ||||||
内容記述 | In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function in the upper half space G : ξ_n>0 and H be the boundary of G, that is, the hyperplane ξ_n=0. Then, denoting by η=(η_1,…, η_<n-1>, 0) the points of the plane H, there exists a non-negative mass distribution υin H and a constant c≧0 such that [numerical formula] where [numerical formula] denotes the surface area of the unit sphere [numerical formula] In this note, we shall present, in §3,a new proof of the above formula (*), which is entirely different from the original proof and seems to be more simple and more natural as compared with the original one. Moreover, as its application, we shall give, in §5,a extremely brief proof for the classical but epoch-making Fatou's therem in the theory of analytic functions and, by means of the real function-theoretic arguments, we shall give, in §6,a delicate variant of the Reflection Princiole due to H. Schwarz. The first two sections 1 and 2 give the prelimiaries for the following treatments. | |||||
書誌情報 |
聖徳学園岐阜教育大学紀要 en : Bulletin of Gifu College of Education 巻 34, p. 79-86, 発行日 1997-09-30 |
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雑誌書誌ID | ||||||
収録物識別子 | AN0011586X | |||||
ISSN | ||||||
収録物識別子 | 09160175 |