Laplace—Stieltjes变换所定义的右半平面上的解析函数的增长性与型函数.pdfVIP

维普资讯 第37卷第2期 数 学 进 展 Vo1．37．NO．2 2007年4月 ADVANCESIN M ATHEMATICS April，2008 On Type-function and Laplace-—StieltjesTransformationsConvergent in theRightH alf-plane KongYinying ， SunDaochun2 (．Dept．ofMath．andComputerScience，GuangdongUniv．ofBusinessStudies，Guangzhou， Guangdong，510320,P．R．Chinba； 2．SchoolofMath．SciencesofSouthChinaNormalUniv．， GuangzhouIGuangdongI510631，P．R．Chinn) Inthispaper，wefirstintroduceProximateorderandType—functionU(r)foranalytic functionsoffiniteorderrepresentedbyLaplace—StieltjestransformationsF(s)convergentonly intherighthalf-plane，andinvestigatethegrowth ofsuchfunctions．Someresultssimilarto Dirichletseriesareobtained． Keywords：Laplace—Stieltjestransformations；order；proximateorder；type—function MR(2000)subjectclassification：44A10；30D15／CLCnumber：O177．4：O174．52 Documentcode：A ArticleID：1000--0917(2008)02．．0197．09 0 Introduction Yu Jiarong[ Knopp and Sun Daochun investigatedthegrowth and thedistribution of ， valuesofDirichletseries∑ 1ane一)、n(s=盯+it，0≤ 1 2 3 nT+。。，盯，t∈} foralongtimeandobtainedmanyimportantresults[2,3] ． Fromtheresearchofthepapersof[4】and[5】jDirichletserieswasregardedasaspecial exampleofLaplace—Stieltjestransformations．In1963，YuJiarong[6』extenttheresultsof4『，51and establishedtheValiron—Knopp—Bohrformulasoftheassociatedabscissasofboundedconvergence． absoluteconvergenceanduniformconvergenceofLaplace—Stieltjes．Moreover，hefirstintroduced (盯，F)，(盯，F)andorderofanalyticfunctionsrepresentedbyL—Stransformsandobtained som