2021-12-07T21:49:26Zhttps://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:000395142021-03-01T14:09:19Z
Propagation of microanalyticity at the boundary for solutions of linear differential equationsGiuseppe, Zampieri138186410application/pdfLet $M = R^n$, $iS*M = R^n \times iS^{n - 1}$. 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 ; its proof is a consequence of the results of  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.departmental bulletin paperFaculty of Science, The University of Tokyo1986-10-15application/pdfJournal 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233429439AA006979670040-8980https://repository.dl.itc.u-tokyo.ac.jp/record/39514/files/jfs330210.pdfeng