In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between t...In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.展开更多
The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane.By introducing the concept of generalized order,we obtain...The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane.By introducing the concept of generalized order,we obtain two equivalence theorems of Laplace-Stiettjes transforms related to the generalized order,A_(n)^(*)andλ_(n).The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform.We also obtain some theorems about the generalized order,the error,and the coefficients of Laplace-Stieltjes transforms,which are generalization and improvement of the previous results.展开更多
In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in term...In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.展开更多
In the paper, the α-order of the Laplace-Stieltjes Transform is introducedfirstly, then we get the relationship between α-order represented by the maximum modulus and α-order represented by A^*n, λn. Lastly, we ob...In the paper, the α-order of the Laplace-Stieltjes Transform is introducedfirstly, then we get the relationship between α-order represented by the maximum modulus and α-order represented by A^*n, λn. Lastly, we obtain the relationship between type τrepresented by the maximum modulus and type τ represented by A^*n, λn.展开更多
In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
文摘In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.
基金supported by the National Natural Science Foundation of China (11561033)the Natural Science Foundation of Jiangxi Province in China (20181BAB201001)+4 种基金the Foundation of Education Department of Jiangxi (GJJ190876, GJJ190895,GJJ202303) of Chinasupported by Guangdong Natural Science Foundation(2018A030313954)Guangdong University (New Generation Information Technology) Key Field Project(2020ZDZX3019)Project of Guangdong Province Innovative Team (2020WCXTD011)Guangdong Provincial Government’s project “Promoting the construction of the Guangdong-Hong Kong-Macao Greater Bay Area and building a new open economic system”.
文摘The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane.By introducing the concept of generalized order,we obtain two equivalence theorems of Laplace-Stiettjes transforms related to the generalized order,A_(n)^(*)andλ_(n).The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform.We also obtain some theorems about the generalized order,the error,and the coefficients of Laplace-Stieltjes transforms,which are generalization and improvement of the previous results.
文摘In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.
基金Supported by National Natural Science Foundation of China (Grant No. 11661044)。
文摘In the paper, the α-order of the Laplace-Stieltjes Transform is introducedfirstly, then we get the relationship between α-order represented by the maximum modulus and α-order represented by A^*n, λn. Lastly, we obtain the relationship between type τrepresented by the maximum modulus and type τ represented by A^*n, λn.
基金Foundation item： the National Natural Science Foundation of China （No. 10471048） Specialized Research Fund for the Doctoral Program of Higher Education （No. 20050574002）.
文摘In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
