The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
Let and A be the generator of an -times resolvent family on a Banach space X. It is shown that the fractional Cauchy problem has maximal regularity on if and only if is of bounded semivariation on .
In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteri...In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for α-times resolvent operator families.展开更多
In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded...In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.展开更多
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
There are some researchers considering the problem whether A-1 is the generator of a bounded C0-semigroup if A generates a bounded C0-semigroup. Actually, it is a very basic and important problem. In this paper, we di...There are some researchers considering the problem whether A-1 is the generator of a bounded C0-semigroup if A generates a bounded C0-semigroup. Actually, it is a very basic and important problem. In this paper, we discuss whether -A-1 is the generator of a bounded α-times resolvent family if -A generates a bounded α-times resolvent family.展开更多
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘Let and A be the generator of an -times resolvent family on a Banach space X. It is shown that the fractional Cauchy problem has maximal regularity on if and only if is of bounded semivariation on .
基金Supported by the National Natural Science Foundation of China (Grant No.10971146)
文摘In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for α-times resolvent operator families.
文摘In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
文摘There are some researchers considering the problem whether A-1 is the generator of a bounded C0-semigroup if A generates a bounded C0-semigroup. Actually, it is a very basic and important problem. In this paper, we discuss whether -A-1 is the generator of a bounded α-times resolvent family if -A generates a bounded α-times resolvent family.
