多重Laplace-Stieltjes变换的两个等式  

Two Equalities of Multiple Laplace-Stieltjes Transform

作　　者：毕家烨 霍颖莹[1] Bi Jia-ye;Huo Ying-ying(School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学应用数学学院,广东广州510520

出　　处：《广东工业大学学报》2021年第1期82-88,共7页Journal of Guangdong University of Technology

基　　金：国家自然科学基金资助项目(11501127);广东省自然科学基金资助项目(2018A030313954)。

摘　　要：受Dirichlet级数的增长性研究的一个重要等式启发,把相应结果推广到多重Laplace-Stieltjes变换,并得到一个形式优美的等式,类似于内积空间中的Parseval等式。Inspired by an important equality in the study of the growth of Dirichlet series,the corresponding results are generalized in this paper by invoking some properties of functions of bounded Vitali variation,some properties of Riemann-Stieltjes integral and some results from real analysis.Moreover,a well-formed equality is obtained,which is similar to the Parseval’s equality in the inner product space.

关 键 词：LAPLACE-STIELTJES变换 DIRICHLET级数 全变差 RIEMANN-STIELTJES积分 

分 类 号：O174.52[理学—基础数学]