Exponential Formula,Perturbation And Approximation Of N-th Order ?-Times Integral C-semigroups

Semigroup theory of operators is an important part of classical operator theory.This thesis mainly uses the research method of operator semigroup theory and the related characteristics of n-th order ?-th times integral C-semigroup,studies the exponential formula of n-th order ?-th times integral C-semigroup,and then demonstrates the compactness of n-th order ?-times integral C-semigroup,the exponential boundedness of disturbance and approximation and other related theories.The results of n-th order ?-times integral C-semigroup are improved and the research content of operator semigroup theory is enriched.This thesis consists of the following four parts:In the first part,the exponential formula of n-th order ?-times integral C-semigroups is discussed.The relationship between n-th order ?-times integral C-semigroups and its discussed,and the exponential formula of n-th order ?-times integral C-semigroups is obtained by combining the resolvent equation of n-th order?-times integral C-semigroup.In the second part,the compactness of n-th order ?-times integral C-semigroups is studied.Firstly,the definition of compactness of n-th order ?-times integral C-semigroups is given;Secondly,it is proved that if the proposition is n-th order ?-times integral C-semigroups are compact,then the semigroups are mutually continuous according to the topological continuity of uniform operators.In the third part,the exponential boundedness of disturbances of n-th order ?-times integral C-semigroups is studied.This thesis estimates the exponential boundedness of the new semigroup obtained by the generator of n-th order ?-times integral C-semigroups under the disturbance of bounded linear operator,and makes a difference between the new semigroups and original semigroups,so as to obtain two important results.In the fourth part,the approximation of n-th order ?-times integral C-semigroups is discussed.By using the inverse Laplace transform of n-th order ?-times integral C-semigroups,it is proved that if two bounded operators generate n-th order ?-times integral C-semigroups separately,and a semigroup approximates another semigroup,the corresponding presolutions of semigroups are also approximated to each other.