微分算子的半群与谱

Abstract：This project is concerned with the systematic study of some problems.on semigroups and spectra of differential operators, which contains to establish a.theory of semigroup method of non-elliptic differential operators, to apply the semigroup method to Shilov’s parabolic systems and Petrovskij’s correct systems, to obtain some spectral properties of differential operators appeared in mathematical physics, and to give some perfect results for the spectrum of general differential.operators with constant coefficients in Hardy spaces. Some works on the theory of.operator semigroups, ill-posed problems, and singular integral operators are also done. Those works strongly push the theory of differential operators forward. The plan of this project has been fairly finished. 20 papers were published, in which 11 papers were appeared in international journals and 9 papers were included in SCI.

本项目系统研究微分算子半群与谱的若干基本理论问题，包括建立非椭圆微分算子的理论体系；获得Lp谱独立性及扰动的若干一般结果，并应用与微分算子；给出奇异连续谱结构性方面的结果，特别是解决到Kato位势的Schrodinger算子奇异连续谱的问题。其意义在于有力赝贫⒎炙阕右话憷砺鄣慕徊酵晟疲⑽湓诹孔恿ρУ确矫嬗τ霉ぷ鞯目沟於ɑ