In order to enrich the theory of semigroups,classical methods in operator semigroups theory and definition of two-parameter C_0 semigroups are introduced,and some of one-parameter C_0 semigroups properties are generalized to get some properties of two parameter C_0 semigroups.
为了丰富半群理论,利用经典的算子半群理论中的方法和双参数C0半群的概念,将单参数的C0半群的一些性质推广到双参数的C0半群,得到双参数的C0半群、生成元及其预解式的一些基本结果。
It proves the transport operator generates a strongly continuous group and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the C0 group, and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which has a finite algebraic multiplicity in trip ?, a.
证明了这类迁移算子产生C0群和该群的Dyson-Phillips展开式的二阶余项是紧的,从而得到了该迁移算子的谱在区域Γ中仅由有限个具有限代数重数的离散本征值组成和占优本征值的存在性等结果。
It proves the transport operator generates a C_0 group and the second-order remained term of the Dyson-Phillips expansion for the C_0 group is compact in L~p(1<p<∞) space and weakly compact in L~1 space,and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite algebra.
在Lp(1 p<∞)空间研究了板模型中具周期边界条件下各向异性、连续能量、均匀介质的迁移算子的谱,证明了:这类迁移算子产生C0群的Dyson—Phillips展开式的二阶余项在Lp(1