A New Proof of Global SmoothingEstimates for Dispersive Equations
A New Proof of Global SmoothingEstimates for Dispersive Equations
复制标题
色散方程全局平滑估计的新证明
DOI：
10.1007/978-3-0348-7840-1_3
复制
发表时间：
2004
影响因子：
0.6
通讯作者：
M. Sugimoto
中科院分区：
文献类型：
--
作者：
Michael Ruzhansky;M. Sugimoto
本文的目的是提供一种新的方法来证明色散方程如薛定谔方程的全局平滑估计。为此，通过正则变换建立了一类傅里叶积分算子形式的egorov型定理，并证明了它们的加权l2有界性。先前的结果如Asada和Fujiwara(1)没有涵盖有界性结果。通过使用它们，为Ben-Artzi & Klainerman(2)的结果提供了一种不同的证明。这一新思想使人们对色散方程的平滑效应有了清晰的认识，并有望进一步发展。实际上，还公布了一些基于相同思想的扩展结果。数学学科分类（2000）。主35Q40j次35B65。
The aim of this article is to provide a new method to prove global smoothing estimates for dispersive equations such as Schrodinger equations. For the purpose, the Egorov-type theorem via canonical transformation in the form of a class of Fourier integral operators is established, and their weighted L 2-boundedness is also proved. The boundedness result is not covered by previous one such as Asada and Fujiwara (1). By using them, a different proof for the result obtained by Ben-Artzi & Klainerman (2) is provided. This new idea gives a clear understanding of smoothing effects of dispersive equations, and further developments are also expected. In fact, some extended results based on the same idea are also announced. Mathematics Subject Classification (2000). Primary 35Q40j Secondary 35B65.