Microlocal analytic smoothing effect for the Schrodinger equation
Microlocal analytic smoothing effect for the Schrodinger equation
复制标题
薛定谔方程的微局域解析平滑效应
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
C. Zuily
中科院分区：
文献类型：
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作者：
Luc Robbiano;C. Zuily
0.引言和主要结果。本文研究变系数线性薛定谔方程初值问题解的微局部解析光滑性。其目的是将初始数据在无穷远处的行为与微局部解析光滑性联系起来;这种现象被称为微局部光滑效应。本文给出的结果是Craig-Kappeler-Strauss [CKS]，[C]关于C ∞情形的解析结果的推广.然而，我们的方法证明，这依赖于Sjöstrand理论[Sj]，是完全不同的[CKS]。近年来，Shananin [Sh]、Kapitanski-Safarov [KS]和Wunsch [W]的论文也研究了这个问题。Doi [D1]、[D2]也得到了相关结果，我们参考了[CKS]的论文以获得更多关于该主题的参考文献。让我们描述一下我们的主要结果。设P = P（y，Dy）是R中的二阶微分算子，
0. Introduction and main results. The purpose of this work is to study the microlocal analytic smoothness of solutions of the initial value problem for the linear Schrödinger equation with variable coefficients. The aim is to relate the behavior at infinity of the initial data with the microlocal analytic smoothness; this phenomenon is known as themicrolocal smoothing effect. The results presented here are extensions to the analytic case of those of Craig-Kappeler-Strauss [CKS], [C], which concern theC∞ case. However, our method of proof, which relies on Sjöstrand theory [Sj], is entirely different from that of [CKS]. This question has also been investigated in recent years in the papers of Shananin [Sh], Kapitanski-Safarov [KS], and Wunsch [W]. Related results have also been obtained by Doi [D1], [D2], and we refer to the paper [CKS] for more references on the subject. Let us describe our main result. Let P = P(y,Dy), a second-order differential operator inR,