Analysis Of Properties On Two Parameter Semi-group

In this paper, the definition of two-parameter C₀semigroup generated by thebounded linear operators on two Banach spaces is given, and the condition of existenceof two-parameter C₀semigroup is given. The paper discusses the strong continuity, itsproperty of two-parameter C₀semigroup, and the property of differential and integral.According to the property related, the paper discusses the boundary of two-parameter C₀semigroup. The concept of infinitesimal generator is given, and its properties arediscussed. Furthermore, according to the concept of infinitesimal generator, the conceptof resolvent and its property is discussed. In order to discuss the determination betweentwo-parameter C₀semigroup and its infinitesimal generator, Hille-Yosida theorem isproposed.The definition of two-parameter semigroup generated by the bounded linearoperators on two Banach spaces is given, and a new definition about boundary isproposed. And also, the continuity of two-parameter semigroup is discussed. In thispaper, the definition of resolvent of two-parameter semigroup is given, and its boundaryis discussed. The definition of infinitesimal generator of two-parameter semigroup isgiven, the relationship between infinitesimal generator and differential operator isdiscussed. This paper discusses the decisive relationship between Markov process andtwo-parameter semigroup, and also discusses the property of Quasi–Homogeneous.