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

doi:10.1007/s10473-021-0222-1

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 646-656.doi: 10.1007/s10473-021-0222-1

• 论文 • 上一篇

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

徐洪焱¹, 孔荫莹²

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

收稿日期:2020-04-09 修回日期:2020-10-26 出版日期:2021-04-25 发布日期:2021-04-29
通讯作者: Yinying KONG E-mail:kongcoco@hotmail.com
作者简介:Hongyan XU,E-mail:xhyhhh@126.com
基金资助:
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".

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".

摘要/Abstract

摘要： 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.

关键词: Laplace-Stieltjes transform, order, error, growth

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

中图分类号:

30D15

徐洪焱, 孔荫莹. ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER[J]. 数学物理学报(英文版), 2021, 41(2): 646-656.

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.

参考文献

[1] Batty C J K. Tauberian theorem for the Laplace-Stieltjes transform. Trans Amer Math Soc, 1990, 322(2):783-804
[2] Chern Peter T Y. On meromorphic functions with finite logarithmic order. Trans Amer Math Soc, 2006, 358(2):473-489
[3] Juneja O P, Kapor G P, Bajpai S K. On the (p, q)-order and lower (p, q)-order of an entire function. J Reine Angew Math, 1976, 282:53-67
[4] Knopp K. Über die Konvergenzabszisse des Laplace-Integrals. Math Z eits, 1951, 54:291-296
[5] Kong Y Y. Laplace-Stieltjes transforms of infinite order in the right half-plane. Acta Math Sinica, 2012, 55:141-148
[6] Kong Y Y, Sun D C. On the growth of zero order Laplace-Stieltjes transform convergent in the right half-plane. Acta Mathematica Scientia, 2008, 28B(2):431-440
[7] Kong Y Y. The Laplace-Stieltjes transform of infinite order in the whole complex plane. Acta Math Sinica, 2013, 56A(1):53-60
[8] Luo X, Liu X Z, Kong Y Y. The regular growth of Laplace-Stieltjes transforms. J of Math (PRC), 2014, 34:1181-1186
[9] Luo X, Kong Y Y. On the order and type of Laplace-Stieltjes transforms of slow growth. Acta Mathematica Scientia, 2012, 32A:601-607
[10] Mishkelyavichyus A. A Tauberian theorem for the Laplace-Stieltjes integral and the Dirichlet series (in Russian). Litovsk Mast Sb, 1989, 29(4):745-753
[11] Sato D. On the rate of growth of entire functions of fast growth. Bull Amer Math Soc, 1963, 69:411-414
[12] Singhal C, Srivastava G S. On the growth and approximation of entire functions represented by LaplaceStieltjes transformation. Ann Univ Ferrara, 2017, 63:365-376
[13] Shang L N, Gao Z S. The growth of entire functions of infinite order represented by Laplace-Stieltjes transformation. Acta Mathematica Scientia, 2007, 27(6):1035-1043
[14] Shang L N, Gao Z S. The value distribution of analytic functions defined by Laplace-Stieltjes transforms. Acta Math Sinica, 2008, 51A(5):993-1000
[15] Sheremeta M M. Asymptotical behaviour of Laplace-Stiltjes integrals//Mathematical Studies, 15. Lviv, VNTL Publishers, 2010
[16] Widder D V. The Laplace transform. Princeton, NJ:Princeton University Press, 1946
[17] Xu H Y, Liu S Y. The approximation of Laplace-Stieltjes transforms with finite order. Journal of Inequalities and Applications, 2017, 164:1-14
[18] Xu H Y, Kong Y Y. The approximation of Laplace-Stieltjes transformations with finite order on the left half plane. Comptes Rendus Mathematique, 2018, 356:63-76
[19] Yu J R. Borel's line of entire functions represented by Laplace-Stieltjes transformation. Acta Math Sinica, 1963, 13:471-484
[20] Yu J R. Dirichlet series and the random Dirichlet series. Beijing:Science Press, 1997

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

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

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