Perturbed Two Parameter C Semigroups And Two Parameter Bounded Operator C Groups

According to the nature of two parameter C semigroups and its infinitesimal generator, the nature such as approximation and perturbation, and the nature of two parameter C0 bounded operator groups, then contacting norm continuity and immediate compactness of operator, using classical methods of operator semigroups, the nature of perturbed two parameter C semigroups and the nature of two parameter bounded operator C groups are studied in this paper. This article includes the following sections:Part 1: Depending on the perturbation nature of two parameter C semigroups and the nature of immediate norm continuity of operators, it’s proposed and demonstrated that perturbed two parameter C semigroups maintained immediate norm continuity of the original two parameter C semigroups. Finally, it’s discovered that immediate norm continuity of perturbed two parameter C semigroups.Part 2: In order to study C semigroups, two parameter C semigroups, perturbed two parameter C semigroups and so on, it’s proposed and demonstrated that perturbed two parameter C semigroups maintained norm continuity and absolute compactness of the original two parameter C semigroups in this part. And then it’s discovered that norm continuity and absolute compactness of perturbed two parameter C semigroups.Part 3: According to the nature of two parameter C semigroups and one parameter C groups, then contacting the nature of two parameter C0 bounded operator groups and its infinitesimal generator, it’s obtained that the concept of two parameter bounded operator C groups and its infinitesimal generator. Secondly, it’s proposed the nature of two parameter bounded operator C groups and its infinitesimal generator and demonstrated the generation theorem of two parameter bounded operator C groups. Finally, using the nature of two parameter bounded operator C groups and its infinitesimal generator, it’s proposed and demonstrated that the relationship between two parameter bounded operator C groups and two parameter C semigroups and the relationship between two parameter bounded operator C groups and C groups.