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

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, A *n 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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Acknowledgements

Congratulations to Professor Yu Jiarong on his 100th birthday! Yinying Kong would like to express his sincere thanks to Professor Min Ru for his valuable information during his study at the Mathematics Department of University of Houston.

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Correspondence to Yinying Kong.

Additional information

The first author was supported by the National Natural Science Foundation of China (11561033), the Natural Science Foundation of Jiangxi Province in China (20181BAB201001), and the Foundation of Education Department of Jiangxi (GJJ190876, GJJ190895, GJJ202303) of China. The second author was supported by Guangdong Natural Science Foundation (2018A030313954), Guangdong University (New Generation Information Technology) Key Field Project (2020ZDZX3019), Project of Guangdong Province Innovative Team (2020WCXTD011) and Guangdong Provincial Government’s project “Promoting the construction of the Guangdong-Hong Kong-Macao Greater Bay Area and building a new open economic system”.

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Xu, H., Kong, Y. Entire Functions Represented by Laplace-Stieltjes Transforms Concerning the Approximation and Generalized Order. Acta Math Sci 41, 646–656 (2021). https://doi.org/10.1007/s10473-021-0222-1

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Key words

  • Laplace-Stieltjes transform
  • order
  • error
  • growth

2010 MR Subject Classification

  • 30D15
  • 44A10