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Propagation of microanalyticity at the boundary for solutions of linear differential equations
https://doi.org/10.15083/00039505
https://doi.org/10.15083/00039505978b498f-8944-4abf-bec3-5fe63d8051d8
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jfs330210.pdf (472.6 kB)
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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 | Propagation of microanalyticity at the boundary for solutions of linear differential equations | |||||
| 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 | 10.15083/00039505 | |||||
| ID登録タイプ | JaLC | |||||
| 著者 |
Giuseppe, Zampieri
× Giuseppe, Zampieri |
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| 著者所属 | ||||||
| 著者所属 | Department de Mathematiques CSP Univ. | |||||
| 著者所属 | ||||||
| 著者所属 | Istituto di Analisi dell'Universita | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let $M = R^n$, $iS*M = R^n \times iS^{n - 1}$. For coordinates $(x + i\eta ) = (x_1 ,x';i\eta _1 ,i\eta ')$ in $iS*M$, we set $N = \left\{ {x_1 = 0} \right\},M^ + = \left\{ {x_1 \geqslant 0} \right\},S^{n - 2}=\left\{ {i\eta _1 = 0} \right\},iS*N = R^{n - 1} \times iS^{n - 2} $. Let $P = P(D)$ be a differential operator with constant coefficients and order m for which N is non-characteristic. Let $A_M $ be the sheaf of real analytic functions on M, denote by $A_M^P $ the kernel sheaf of P, and, for $u \in \Gamma (U \cap \mathop {M^ + }\limits^ \circ ,A_M^P ),U \subset M$ open, let $\gamma (u)$ be the m traces of u on $U \cap N$. For $(x'+i\eta') \in iS*N$ with $(0,x') \in U$ we discuss the condition : $(0,1)$ $(x',i\eta ') \ otin SS\gamma (u)$ for any $u \in \Gamma (U \cap \mathop {M^+ }\limits^ \circ ,A_M^P )$. We prove that ""$ - \eta '$-semihyperbolicity"" to $N^ + $ of P implies $(0,1)$. Under some additional hypotheses we also prove the converse. The first part of the statement was conjectured by Kaneko in [2]; its proof is a consequence of the results of [11] on N-regularity"" of non-microcharacteristic operators. The second part is obtained by means of a microlocallynull solution. I wish to thank Prof. P. Schapira for frequent and invaluable discussions on this subject. |
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| 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 33, 号 2, p. 429-439, 発行日 1986-10-15 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 0040-8980 | |||||
| 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Scheme | NDC | |||||
| 主題 | 410 | |||||
| Mathematical Reviews Number | ||||||
| MR0866400 (88a:35015) | ||||||
| 出版者 | ||||||
| 出版者 | Faculty of Science, The University of Tokyo | |||||
