无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 556-568.

无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近

徐洪焱^1,^2,*(),刘三阳²

¹ 上饶师范学院数学与计算机学院江西上饶 334001
² 西安电子科技大学数学与统计学院西安 710126

收稿日期:2019-04-23 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 徐洪焱 E-mail:xhyhhh@126.com
基金资助:
国家自然科学基金(11561033);国家自然科学基金(61877046);江西省自然科学基金(20181BAB201001);江西省教育厅科学技术项目(GJJ180734);江西省教育厅科学技术项目(GJJ180735)

The Approximation and Growth of Entire Function Represented by Laplace-Stieltjes Transform with Infinite Order

Hongyan Xu^1,^2,*(),Sanyang Liu²

¹ School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001
² School of Mathematics and Statistics, Xidian University, Xi'an 710126

Received:2019-04-23 Online:2020-06-26 Published:2020-07-15
Contact: Hongyan Xu E-mail:xhyhhh@126.com
Supported by:
the NSFC(11561033);the NSFC(61877046);the NSF of Jiangxi Province(20181BAB201001);the Foundation of Education Department of Jiangxi(GJJ180734);the Foundation of Education Department of Jiangxi(GJJ180735)

摘要/Abstract

摘要：

通过引入双下q-型的概念，讨论了具有非正规增长的全平面收敛的Laplace-Stieltjes变换的增长性与逼近，得到了Laplace-Stieltjes变换的尾项与双下q-型，A_n^*以及λ_n的关系定理，推广了罗茜，孔荫莹，Singhal与Srivastava等的结果.

关键词: Laplace-Stieltjes变换, 逼近, q-非正规增长

Abstract:

The main purpose of this article is to investigate the growth and approximation of Laplace-Stieltjes transform with irregular growth converges in the whole plane, by introducing the concept of the double lower q-type. We obtain some relation theorems concerning the double lower q-type, the error, A_n^* and λ_n, which are extension and improvement of the previous theorems given by Luo-Kong, Singhal-Srivastava.

Key words: Laplace-Stieltjes transform, Approximation, Double lower q-type

中图分类号:

O174

徐洪焱,刘三阳. 无限级Laplace-Stieltjes变换所表示的整函数的增长性与逼近[J]. 数学物理学报, 2020, 40(3): 556-568.

Hongyan Xu,Sanyang Liu. The Approximation and Growth of Entire Function Represented by Laplace-Stieltjes Transform with Infinite Order[J]. Acta mathematica scientia,Series A, 2020, 40(3): 556-568.

参考文献 29

1	Batty C . Tauberian theorem for the Laplace-Stieltjes transform. Trans Amer Math Soc, 1990, 322 (2): 783- 804 doi: 10.1090/S0002-9947-1990-1013326-6
2	Ding X Q , Yu J R . Picard points of random Dirichlet series. Bull Sci Math, 2000, 124 (3): 225- 238 doi: 10.1016/S0007-4497(00)00134-2
3	Huo Y Y , Kong Y Y . On generalized orders and generalized types of Dirichlet series in the right half-plane. Acta Math Sci, 2014, 34B (1): 175- 182
4	Knopp K . Über die Konvergenzabszisse des Laplace-integrals. Math Zeits, 1951, 54, 291- 296 doi: 10.1007/BF01574830
5	孔荫莹. 半平面解析的无穷级Laplace-Stieltjes变换. 数学学报, 2012, 55A (1): 141- 148
	Kong Y Y . Laplace-Stieltjes transform of infinite order in the right half-plane. Acta Math Sinica, 2012, 55A (1): 141- 148
6	孔荫莹, 霍颖莹. 右半平面解析的Laplace-Stieltjes变换的广义级与型. 数学学报, 2016, 59A, 91- 98 doi: 10.3969/j.issn.1005-3085.2016.01.009
	Kong Y Y , Huo Y Y . On generalized orders and types of Laplace-Stieltjes transformas analytic in the right half-plane. Acta Math Sinica, 2016, 59A, 91- 98 doi: 10.3969/j.issn.1005-3085.2016.01.009
7	Kong Y Y , Hong Y . On the Growth of Laplace-Stieltjes Transforms and the Singuar Direction of Complex Analysis. Jinan: Jinan University Press, 2010
8	Kong Y Y , Sun D C . On the growth of zero order Laplace-Stieltjes transform convergent in the right half-plane. Acta Math Sci, 2008, 28B (2): 431- 440
9	Kong Y Y , Yang Y . On the growth properties of the Laplace-Stieltjes transform. Complex Variables and Elliptic Equations, 2014, 59, 553- 563 doi: 10.1080/17476933.2013.766174
10	罗茜, 刘兴臻, 孔荫莹. 在全平面上解析的Laplace-Stieltjes变换的正规增长性. 数学杂志, 2014, 34, 1181- 1186
	Luo X , Liu X Z , Kong Y Y . The regular growth of Laplace-Stieltjes transforms. J of Math, 2014, 34, 1181- 1186
11	罗茜, 孔荫莹. 全平面上慢增长的Laplace-Stieltjes变换的级与型. 数学物理学报, 2012, 32A, 601- 607 doi: 10.3969/j.issn.1003-3998.2012.03.016
	Luo X , Kong Y Y . On the order and type of Laplace-Stieltjes transforms of slow growth. Acta Math Sci, 2012, 32A, 601- 607 doi: 10.3969/j.issn.1003-3998.2012.03.016
12	Mishkelyavichyus A . A Tauberian theorem for the Laplace-Stieltjes integral and the Dirichlet series (Russian). Litovsk Mast Sb, 1989, 29 (4): 745- 753
13	Oskolkov V A , Kalinichenko L I . Growth of entire functions represented by Dirichlet series. Sbornik:Mathematics, 1996, 187, 1545- 1560 doi: 10.1070/SM1996v187n10ABEH000168
14	Shang L N , Gao Z S . Entire functions defined by Dirichlet series. J Math Anal Appl, 2008, 339, 853- 862
15	尚丽娜, 高宗升. Laplace-Stieltjes变换所定义的无限级整函数的增长性. 数学物理学报, 2007, 27A (6): 1035- 1043
	Shang L N , Gao Z S . The growth of entire functions of infinite order represented by Laplace-Stieltjes transformation. Acta Math Sci, 2007, 27A (6): 1035- 1043
16	尚丽娜, 高宗升. Laplace-Stieltjes变换所表示的解析函数的值分布. 数学学报, 2008, 51A (5): 993- 1000 doi: 10.3321/j.issn:0583-1431.2008.05.019
	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 doi: 10.3321/j.issn:0583-1431.2008.05.019
17	Sheremeta M N , Fedynyak S I . On the derivative of a Dirichlet series. Siberian Mathematical Journal, 1998, 39 (1): 181- 197 doi: 10.1007/BF02732373
18	Singhal C, Srivastava G S. On the growth and approximation of entire functions represented by Laplace-Stieltjes transformation. Ann Univ Ferrara, 2017, 59(1): 1-12
19	Sun D C . On the distribution of values of random Dirichlet series II. Chinese Ann Math, 1990, 11B (1): 33- 44
20	Tian F J, Sun D C, Yu J R. Sur les séries aléatoires de Dirichlet. C R Acad Sci Paris Ser I, 1998, 326: 427-431
21	Vakarchuk S B, Zhir S I. On some problems of polynomial approximation of entire transcendental functions. Ukrainian Math J, 2002, 54(9): 1393-1401
22	Xu H Y, Xuan Z X. The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane. Journal of Inequalities and Applications, 2013, 2013: Article 273
23	Xu H Y, Xuan Z X. The singular points of analytic functions with finite X-order defined by Laplace-Stieltjes transformations. Journal of Function Spaces 2015, Article ID: 865069
24	Xu H Y, Liu S Y. The approximation of Laplace-Stieltjes transforms with finite order. Journal of Inequalities and Applications 2017, 2017: Artcile 164
25	徐洪焱, 刘三阳. 慢增长的Laplace-Stieltjes变换的逼近. 数学学报, 2019, 62A (3): 457- 468 doi: 10.3969/j.issn.0583-1431.2019.03.011
	Xu H Y , Liu S Y . The approximation of Laplace-Stieltjes transforms with slow growth. Acta Math Sinica, 2019, 62A (3): 457- 468 doi: 10.3969/j.issn.0583-1431.2019.03.011
26	余家荣. Laplace-Stieltjes变換所定义的整函数之Borel线. 数学学报, 1963, 13, 471- 484
	Yu J R . Borel's line of entire functions represented by Laplace-Stieltjes transformation. Acta Math Sinica, 1963, 13, 471- 484
27	余家荣. 狄利克雷级数与随机狄得克雷级数. 北京: 科学出版社, 1997
	Yu J R . Dirichlet Series and the Random Dirichlet Series. Beijing: Science Press, 1997
28	Yu J R . Sur les droites de Borel de certaines fonction entières. Annales École Norm Sup, 1951, 68 (3): 65- 104
29	张洪申, 孙道椿. 右半平面上Laplace-Stieltjes变换的值分布. 数学学报, 2012, 55A (3): 535- 542
	Zhang H S , Sun D C . The value distribution of Laplace-Stieltjes transforms in the right half plane. Acta Math Sinica, 2012, 55A (3): 535- 542

[1]	庞兆鋆,虞旦盛,周平. 移动紧圆盘上Bernstein-Durrmeyer型算子的逼近[J]. 数学物理学报, 2020, 40(3): 545-555.
[2]	王俊俊,杨晓侠. 一类非线性抛物方程H¹-Galerkin混合有限元方法的高精度分析[J]. 数学物理学报, 2019, 39(4): 894-908.
[3]	史艳华,张亚东,王芬玲,赵艳敏,王萍莉. 时间分数阶扩散方程线性三角形元的高精度分析[J]. 数学物理学报, 2019, 39(4): 839-850.
[4]	丘小玲,贾文生. 有限理性下变分不等式的逼近定理[J]. 数学物理学报, 2019, 39(4): 730-737.
[5]	李文霞, 齐秋兰. Baskakov-Kantorovich算子在紧圆盘上的复逼近性质[J]. 数学物理学报, 2018, 38(4): 641-648.
[6]	张厚超, 王俊俊, 石东洋. Extended Fisher-Kolmogorov方程的一类低阶非协调混合有限元方法[J]. 数学物理学报, 2018, 38(3): 571-587.
[7]	张骞, 袁永新. 用加速度和位移反馈修正无阻尼振动系统的一种迭代法[J]. 数学物理学报, 2018, 38(2): 358-371.
[8]	邵光明, 柴晓娟. Navier-Stokes-Fourier方程的可压逼近[J]. 数学物理学报, 2017, 37(6): 1070-1084.
[9]	袁永新, 赵文华, 刘皞. 修正无阻尼结构系统的一种有效迭代法[J]. 数学物理学报, 2016, 36(5): 886-900.
[10]	张厚超, 石东洋. 非线性四阶双曲方程低阶混合元方法的超收敛分析[J]. 数学物理学报, 2016, 36(4): 656-671.
[11]	陆万春, 易才凤. Laplace-Stieltjes变换所表示的解析函数的β -级[J]. 数学物理学报, 2014, 34(5): 1236-1244.
[12]	陈超平, 成军祥. Landau常数的逼近公式[J]. 数学物理学报, 2014, 34(5): 1245-1253.
[13]	邓伟奇. 分层变分包含问题中经由分层不动点途径的黏性方法[J]. 数学物理学报, 2014, 34(5): 1254-1263.
[14]	谭启建, 潘朝毅, 冷忠建. 具边界相交交界面的拟线性椭圆方程组的挠射问题[J]. 数学物理学报, 2014, 34(4): 777-788.
[15]	曹飞龙, 戴腾辉, 张永全. 压缩回归学习算法的泛化界[J]. 数学物理学报, 2014, 34(4): 905-916.