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Entire Functions Represented by Laplace-Stieltjes Transforms Concerning the Approximation and Generalized Order

Authors
  • Xu, Hongyan1
  • Kong, Yinying2
  • 1 Shangrao Normal University, Shangrao, 334001, China , Shangrao (China)
  • 2 Guangdong University of Finance and Economics, Guangzhou, 510320, China , Guangzhou (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jan 29, 2021
Volume
41
Issue
2
Pages
646–656
Identifiers
DOI: 10.1007/s10473-021-0222-1
Source
Springer Nature
Keywords
License
Yellow

Abstract

The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane. By introducing the concept of generalized order, we obtain two equivalence theorems of Laplace-Stieltjes transforms related to the generalized order, An* and λn. The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform. We also obtain some theorems about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms, which are generalization and improvement of the previous results.

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