Analytic wave front for solutions to Schrodinger equation
Analytic wave front for solutions to Schrodinger equation
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薛定谔方程解的解析波前
DOI：
10.1016/j.aim.2009.06.002
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
V
中科院分区：
文献类型：
--
作者：
Martinez;A.;Nakamura;S.;Sordoni;V
本文是[A.马丁内斯，S。中村，V. Sordoni，具有长程扰动的薛定谔方程的解析平滑效应，Comm. Pure Appl. Math. LIX（2006）1330-1351]，其中证明了拉普拉斯H 0对Rn的长程扰动的解析平滑效应。在本文中，我们考虑Rn上拉普拉斯算子的短程型扰动H，并根据自由解的解析波阵面集来表征薛定谔方程解的解析波阵面集：e-itHf：[公式：见文本]，对于t <0 in the forward non-trapping region. The same result holds for t>0在向后非捕获区域。这个结果是Hassel和Wunsch [A. Hassel，J. Wunsch，散射度量的薛定谔传播算子，Ann. of Math.162（2005）487-523]和中村[S.中村，波阵面集解薛定谔方程，J. Funct. Anal. 256（2009）1299-1309]。
This paper is a continuation of [A. Martinez, S. Nakamura, V. Sordoni, Analytic smoothing effect for the Schrödinger equation with long-range perturbation, Comm. Pure Appl. Math. LIX (2006) 1330–1351], where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian H0on Rn. In this paper, we consider short-range type perturbations H of the Laplacian on Rn, and we characterize the analytic wave front set of the solution to the Schrödinger equation: e−itHf, in terms of that of the free solution: [Formula: see text] , for t<0 in the forward non-trapping region. The same result holds for t>0 in the backward non-trapping region. This result is an analytic analogue of results by Hassel and Wunsch [A. Hassel, J. Wunsch, The Schrödinger propagator for scattering metrics, Ann. of Math. 162 (2005) 487–523] and Nakamura [S. Nakamura, Wave front set for solutions to Schrödinger equations, J. Funct. Anal. 256 (2009) 1299–1309].