UTokyo Repository 東京大学
 

UTokyo Repository >
121 数理科学研究科 >
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics >

このページ(論文)をリンクする場合は次のURLを使用してください: http://hdl.handle.net/2261/6436

タイトル: Propagation of microanalyticity at the boundary for solutions of linear differential equations
著者: Giuseppe, Zampieri
発行日: 1986年10月15日
出版者: Faculty of Science, The University of Tokyo
掲載誌情報: Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics, Vol.33(1986), No.2, Page429-439
抄録: 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 : $(0,1)$ $(x',i\eta ') \notin SS\gamma (u)$ 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.
URI: http://hdl.handle.net/2261/6436
ISSN: 0040-8980
出現カテゴリ:Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics

この論文のファイル:

ファイル 記述 サイズフォーマット
jfs330210.pdf461.52 kBAdobe PDF見る/開く

本リポジトリに保管されているアイテムはすべて著作権により保護されています。

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - ご意見をお寄せください