Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can...Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.展开更多
This paper improves Tychonov ford point theorem and discusses the existence of solutions of nonlinear Fredholm integral equations on [0,+∞] in Banach spaces with Frechet space theory.
In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain...In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.展开更多
Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The co...Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The condition is essential for proving the consistency and asymptotic normality of the estimator.展开更多
In this paper we discuss tLhe existence results of the integral solutions to nonlinear evolution inclusion: u' (t) ∈ Au(t) +F(t,u(t)), where A is m-dissipative and F is a set valued map in separable Banach spaces...In this paper we discuss tLhe existence results of the integral solutions to nonlinear evolution inclusion: u' (t) ∈ Au(t) +F(t,u(t)), where A is m-dissipative and F is a set valued map in separable Banach spaces, and extend the relative results in references.展开更多
Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subseq...Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].展开更多
In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamic...In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.展开更多
文摘Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.
文摘This paper improves Tychonov ford point theorem and discusses the existence of solutions of nonlinear Fredholm integral equations on [0,+∞] in Banach spaces with Frechet space theory.
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxmX0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023).
文摘In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.
文摘Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The condition is essential for proving the consistency and asymptotic normality of the estimator.
文摘In this paper we discuss tLhe existence results of the integral solutions to nonlinear evolution inclusion: u' (t) ∈ Au(t) +F(t,u(t)), where A is m-dissipative and F is a set valued map in separable Banach spaces, and extend the relative results in references.
基金Supported by the National Natural Science Founda-tion of China(11790274 and 11871361)partially supported by Qinglan project of Jiangsu Province。
文摘Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxm X0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023)。
文摘In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.
