ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER

doi:10.1007/s10473-021-0222-1

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (2): 646-656.doi: 10.1007/s10473-021-0222-1

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ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER

Hongyan XU¹, Yinying KONG²

1. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, China;
2. Research Institute of Innovation Competitiveness of Guangdong, HongKong and Macao Bay Area(RⅡC), Guangdong University of Finance and Economics, Guangzhou 510320, China

Received:2020-04-09 Revised:2020-10-26 Online:2021-04-25 Published:2021-04-29
Contact: Yinying KONG E-mail:kongcoco@hotmail.com
About author:Hongyan XU,E-mail:xhyhhh@126.com
Supported by:
The first author was supported by the National Natural Science Foundation of China (11561033), the Natural Science Foundation of Jiangxi Province in China (20181BAB201001), and the Foundation of Education Department of Jiangxi (GJJ190876, GJJ190895, GJJ202303) of China. The second author was supported by Guangdong Natural Science Foundation (2018A030313954), Guangdong University (New Generation Information Technology) Key Field Project (2020ZDZX3019), Project of Guangdong Province Innovative Team (2020WCXTD011) and Guangdong Provincial Government's project "Promoting the construction of the Guangdong-Hong Kong-Macao Greater Bay Area and building a new open economic system".

Abstract

Abstract: 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-Stieltjes transforms related to the generalized order, $A_n^*$ and $\lambda_n$. 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.

Key words: Laplace-Stieltjes transform, order, error, growth

CLC Number:

30D15

Hongyan XU, Yinying KONG. ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER[J].Acta mathematica scientia,Series B, 2021, 41(2): 646-656.

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ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER

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