摘要
在L_p(1≤p<+∞)空间中,本文运用半群理论研究了Rotenberg模型中具光滑边界条件的迁移半群的本质谱.采用半群方法和比较算子等方法,证明了对任意的t>0,8>0,算子[U_H(t)-U_0(t)]U_0(s)[U_H(t)-U_0(t)]在L_p(1<p<+∞)在空间中紧和在L_1空间弱紧,得到迁移半群V_H(t)与V_0(t)有相同的本质谱型.
The objective of this paper is to discuss the essential spectrum of transport semigroup with smooth boundary conditions in Retenberg model in Lp（1 ≤ p 〈 ＋∞） space. It is to prove that the operator [UH（t） - U0（t）]U0（s）[UH（t） - U0（t）] is compact in Lp（1 〈 p 〈 ＋∞） space and is weakly compact in L1 space, and it is to obtain that the transport semigroup VH（t） and V0（t） have the same essential spectrum type. The paper relies on theory of semigroups of linear operators, and the main method relies on semigroups and comparison operators.
出处
《应用泛函分析学报》
CSCD
2014年第4期315-321,共7页
Acta Analysis Functionalis Applicata
基金
国家自然科学基金(11461055)
