Results on analytic functions defined by Laplace-Stieltjes transforms with perfect \(\phi\)-type. (English) Zbl 1489.44001
Summary: In this paper, we introduce the concept of the perfect \(\phi\)-type to describe the growth of the maximal molecule of Laplace-Stieltjes transform by using the more general function than the usual. Based on this concept, we investigate the approximation and growth of analytic functions \(F(s)\) defined by Laplace-Stieltjes transforms convergent in the half plane and obtain some results about the necessary and sufficient conditions on analytic functions \(F(s)\) defined by Laplace-Stieltjes transforms with perfect \(\phi\)-type, which are some generalizations and improvements of the previous results given by Y. Kong and Y. Huo [Acta Math. Sin., Chin. Ser. 59, No. 1, 91–98 (2016; Zbl 1363.42008)], C. Singhal and G. S. Srivastava [Anal. Theory Appl. 31, No. 4, 407–420 (2015; Zbl 1349.30125)].
MSC:
| 44A10 | Laplace transform |
| 30D15 | Special classes of entire functions of one complex variable and growth estimates |
References:
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