Journal of Guangdong University of Technology ›› 2021, Vol. 38 ›› Issue (01): 82-88.doi: 10.12052/gdutxb.200025

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Two Equalities of Multiple Laplace-Stieltjes Transform

Bi Jia-ye, Huo Ying-ying   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2012-02-12 Online:2021-01-25 Published:2020-12-21

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Abstract: 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.

Key words: Laplace-Stieltjes transform, Dirichlet series, total variation, Riemann-Stieltjes integration

CLC Number: 

  • O174.52
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