In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weigh...In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).展开更多
In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the...In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the identity operator,and the class of J-symmetric composition operators does not coincide with the class of normal composition operators.In addition,we divide semigroups{φt}of linear fractional self-maps of C+into two classes.We show that the associated composition operator semigroup{Tt}is strongly continuous and identify its infinitesimal generator.As an application,we characterize Jσ-symmetric C0-semigroups of composition operators on A^2(C+).展开更多
This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend...It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.展开更多
In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
文摘In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).
文摘In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the identity operator,and the class of J-symmetric composition operators does not coincide with the class of normal composition operators.In addition,we divide semigroups{φt}of linear fractional self-maps of C+into two classes.We show that the associated composition operator semigroup{Tt}is strongly continuous and identify its infinitesimal generator.As an application,we characterize Jσ-symmetric C0-semigroups of composition operators on A^2(C+).
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
基金Project of Sichuan Provincial Science and Technology Department (No.2007J13-006)
文摘It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
文摘In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
