在右半平面上收斂的Laplace-Stieltjes變換的無(wú)限級(jí)

陸萬(wàn)春,彭友花

(萍鄉(xiāng)高等專科學(xué)校數(shù)學(xué)系,江西 萍鄉(xiāng) 337055)

在右半平面上收斂的Laplace-Stieltjes變換的無(wú)限級(jí)

陸萬(wàn)春,彭友花

(萍鄉(xiāng)高等專科學(xué)校數(shù)學(xué)系,江西 萍鄉(xiāng) 337055)

利用改進(jìn)的較寬松的系數(shù)條件,研究了右半平面上Laplace-Stieltjes變換所表示的解析函數(shù)的增長(zhǎng)性,給出了兩個(gè)充分必要條件,推廣了先前一些文獻(xiàn)的結(jié)果.

Laplace-Stieltjes變換;增長(zhǎng)級(jí);型函數(shù)

1 引言

關(guān)于Laplace-Stieltjes變換所定義的解析函數(shù)增長(zhǎng)性,文獻(xiàn)[1]得到了Valiron-Knopp-Bohr公式,并利用該公式得到了“最大模”和“最大項(xiàng)”的相關(guān)估計(jì),在此基礎(chǔ)上,文獻(xiàn)[2-3]研究了無(wú)限級(jí)的情況.本文在寬松的系數(shù)條件下對(duì)半平面上收斂的Laplace-Stieltjes的無(wú)限級(jí)作進(jìn)一步研究,改進(jìn)了關(guān)于Laplace-Stieltjes變換在收斂半平面上的無(wú)限級(jí)的相關(guān)結(jié)果.

考慮Laplace-Stieltjes變換所定義的函數(shù)

2 引理及證明

3 定理及證明

本文換成較弱的條件(5)和條件(11),改進(jìn)了相關(guān)文獻(xiàn)的結(jié)果.

[1]余家榮.Laplace-Stieltjes變換所定義的整函數(shù)之Borel線[J].數(shù)學(xué)學(xué)報(bào),1963,13(3):471-484.

[2]尚麗娜,高宗升.Laplace-Stieltjes變換所表示的解析函數(shù)的值分布[J].數(shù)學(xué)學(xué)報(bào),2008,51(5):993-1000.

[3]Kong Yinying,Sun Daochun.On type-function and the growth of Laplace-Stieltjes transformations convergent in the right half-plane[J].Adnvance Mathematics,2008,37(2):197-205.

[4]田范基.半平面上的無(wú)限級(jí)隨機(jī)Dirichlet級(jí)數(shù)的值分布[J].數(shù)學(xué)物理學(xué)報(bào),2000,20(2):278-287.

[5]孫道椿.半平面上的隨機(jī)Dirichlet級(jí)數(shù)[J].數(shù)學(xué)物理學(xué)報(bào),1999,19(1):107-112.

[6]余家榮.只在右半平面收斂的指數(shù)級(jí)數(shù)的增長(zhǎng)性及值的分布[J].數(shù)學(xué)年刊,1982,3(5):545-554.

[7]孔蔭瑩.半平面解析的無(wú)窮級(jí)Laplace-Stieltjes變換[J].數(shù)學(xué)學(xué)報(bào),2012,55(1):141-148.

The in fi nite order of Laplace-Stieltjes transformation converging in right plane

Lu Wanchun,Peng Youhua
(Mathematics Department,Pingxiang College,Pingxiang 337055,China)

We studied the growth of analytic functions de fi ned by a Laplace-Stieltjes transformation converging in right plane under a better condition,and established two sufficient and necessary conditions,improved some results in previous references.

Laplace-Stieltjes transform,in fi nite order,type function

O174.5

A

1008-5513(2012)05-0620-08

2012-04-22.

陸萬(wàn)春(1978-),碩士,講師,研究方向：復(fù)分析.

2010 MSC:30D35,44A10