广义薛定谔算子的收敛速度  

The Rate of Convergence on Generalized Schr?dinger Operator

作　　者：何少勇 HE Shaoyong(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;School of Science,Huzhou University,Huzhou,Zhejiang,313000,P.R.China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《数学进展》2021年第5期729-741,共13页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.12071437)。

摘　　要：本文主要考虑了如下定义的广义色散方程{i∂tu+ϕ(√−Δ)u=0,(x,t)∈R×R,u(x,0)=f(x),其中ϕ(√−Δ)是带象征ϕ(|ξ|)的拟微分算子.当象征ϕ满足适当的增长条件和初值f属于Sobolev空间H^(s)(R)时,我们给出了广义色散方程的解点态收敛于初值的收敛速度.这个结论显著推广了最近一些文献的结果.In this paper,we consider the following generalized dispersive equation{i∂tu+ϕ(√−Δ)u=0,(x,t)∈R×R,u(x,0)=f(x),whereϕ(√−Δ)is a pseudo-differential operator with symbolϕ(|ξ|).Whenϕsatisfies suitable growth conditions and the initial data f belongs to the Sobolev space H^(s)(R),we obtain the rate of convergence for solution to the above generalized dispersive equation.This result significantly improves some known results in the literatures.

关 键 词：广义色散方程 SOBOLEV空间 收敛速度 

分 类 号：O174.2[理学—数学]