2024-03-19T10:02:15Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00039565
2022-12-19T04:14:22Z
312:6589:6671:6675
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Microlocal analysis of partial differential operators with irregular singularities
Uchikoshi, Keisuke
138241
410
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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 $\mathop x\limits^ \circ ^*$.
departmental bulletin paper
Faculty of Science, The University of Tokyo
1983-12-10
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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
2
30
299
332
AA00697967
00408980
https://repository.dl.itc.u-tokyo.ac.jp/record/39565/files/jfs300205.pdf
eng