Two-Parameters Bounded Operator C Groups

On the basis of the classical methods of operator semigroups,the concept of two-parameters bounded operator C groups is proposed by combining the research resultsand methods of the predecessors to the operator semigroups,the perturbation,Hille-Yosida theorem,Yosida approximation,approximation problem and spectrummapping theorem of two-parameters bounded operator C groups are studied at the sametime.This paper mainly includes the following four parts:The first part has defines the nature of perturbed two-parameters bounded operator C groups,proved its perturbation theorem and finally obtained its property.The secord part has proved the Yosida theorem and approximation of twoparameters bounded operator C groups.The third part has studied the approximation problem of two parameters bounded operator C groups and obtained generated element sequence limit and the limit of two-parameters bounded operator C groups.The last part has given the concepts of point spectrum,continous spectrum and residual spectrum of two-parameters bounded operator C groups,and proved that the spectrum mapping theorem for two-parameters bounded operator C groups is authentic.