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Sect. 1 A, Mathematics = 東京大学理学部紀要. 第1類A, 数学"}]}]}, "item_4_description_13": {"attribute_name": "フォーマット", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_4_description_5": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "We denote the variables in $R^{n + 1}$ by $x=(x_0 ,x^\u0027)$, where $x_0 \\in R$ and $x^\u0027 \\in R^n$. We consider partial differential operators of the form $P(x,\\partial /\\partial x) = \\sum\\limits_{\\left| \\alpha \\right| \\leqslant m} {a_\\alpha } (x)x_0^{\\kappa (\\left| \\alpha \\right|)} (\\partial /\\partial x)^\\alpha $, where $\\kappa (j)$ is some integer $ \\geqslant 0$, $a_\\alpha (x)$ is real analytic in a neighborhood of $x=0$, and $a_{(m,0, \\ldots ,0)}=1$. We define the irregularity $\\iota \\in \\left[ {1,\\infty )} \\right.$ and the characteristic exponents $\\lambda _1 , \\ldots ,\\lambda _{\\kappa (m)} \\in C$ of the operator P at the point $\\mathop x\\limits^ \\circ ^* = (0;\\sqrt { - 1} ,0, \\ldots ,0) \\in \\sqrt { - 1} T*R^{n + 1}$. 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Microlocal analysis of partial differential operators with irregular singularities
https://doi.org/10.15083/00039556
https://doi.org/10.15083/00039556e2458c14-0bff-4cc3-bc6d-b5e6fe570953
名前 / ファイル | ライセンス | アクション |
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jfs300205.pdf (1.0 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2007-05-15 | |||||
タイトル | ||||||
タイトル | Microlocal analysis of partial differential operators with irregular singularities | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.15083/00039556 | |||||
ID登録タイプ | JaLC | |||||
著者 |
Uchikoshi, Keisuke
× Uchikoshi, Keisuke |
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著者所属 | ||||||
著者所属 | Department of Mathematics Faculty of Science University of Tokyo | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We denote the variables in $R^{n + 1}$ by $x=(x_0 ,x^')$, where $x_0 \in R$ and $x^' \in R^n$. We consider partial differential operators of the form $P(x,\partial /\partial x) = \sum\limits_{\left| \alpha \right| \leqslant m} {a_\alpha } (x)x_0^{\kappa (\left| \alpha \right|)} (\partial /\partial x)^\alpha $, where $\kappa (j)$ is some integer $ \geqslant 0$, $a_\alpha (x)$ is real analytic in a neighborhood of $x=0$, and $a_{(m,0, \ldots ,0)}=1$. We define the irregularity $\iota \in \left[ {1,\infty )} \right.$ and the characteristic exponents $\lambda _1 , \ldots ,\lambda _{\kappa (m)} \in C$ of the operator P at the point $\mathop x\limits^ \circ ^* = (0;\sqrt { - 1} ,0, \ldots ,0) \in \sqrt { - 1} T*R^{n + 1}$. It will be proved that if $\iota >1$ and all the characteristic exponents of P are distinct, then P is equivalent microlocally to the operator $x_0^{k(m)} :C_{R^{n + 1} } \to C_{R^{n + 1} }$ $u \to x_0^{k(m)} u$ in a neighborhood of $\mathop x\limits^ \circ ^*$. | |||||
書誌情報 |
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics = 東京大学理学部紀要. 第1類A, 数学 巻 30, 号 2, p. 299-332, 発行日 1983-12-10 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00408980 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00697967 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 410 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR0722499 (85e:58139) | ||||||
出版者 | ||||||
出版者 | Faculty of Science, The University of Tokyo |