We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some...We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.展开更多
In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.展开更多
By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For expone...By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.展开更多
文摘We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
文摘By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.
