Entire functions of bernstein's class that are not fourier-stieltjes transforms

1997 ◽  
Vol 61 (3) ◽  
pp. 301-312
Author(s):  
A. M. Sedletskii
Keyword(s):  
Entire Functions ◽  
Stieltjes Transforms

scholarly journals Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong Qin Cui ◽  
Hong Yan Xu
Keyword(s):  
Complex Plane ◽  
Entire Functions ◽  
Equivalence Theorem ◽  
Stieltjes Transform ◽  
Proximate Order ◽  
Growth Of Entire Functions ◽  
Stieltjes Transforms

One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of Laplace-Stieltjes transforms is obtained. Besides, the second purpose of this paper is to investigate the approximation of entire functions defined by Laplace-Stieltjes transforms with p,q-proximate order, and some results about the p,q-proximate order, the error, and the coefficients of Laplace-Stieltjes transforms are obtained, which are generalization and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.

scholarly journals The Approximation of Laplace-Stieltjes Transforms Concerning Sun’s Type Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xia Shen ◽  
Hong Yan Xu
Keyword(s):  
Complex Plane ◽  
Infinite Order ◽  
Entire Functions ◽  
Point Of View ◽  
Type Function ◽  
Stieltjes Transforms

The main aim of this paper is to establish some theorems concerning the error E n F , β , the Sun’s type function U r , and M u σ , F of entire functions defined by Laplace-Stieltjes transforms with infinite order converge in the whole complex plane. Our results exhibit the growth of Laplace-Stieltjes transforms from the point of view of approximation.

scholarly journals The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wen Ju Tang ◽  
Jian Chen ◽  
Hong Yan Xu
Keyword(s):  
Finite Order ◽  
Complex Plane ◽  
Infinite Order ◽  
Entire Functions ◽  
Growth Order ◽  
Stieltjes Transform ◽  
Proximate Order ◽  
Growth Of Entire Functions ◽  
Stieltjes Transforms

In this article, we discuss the growth of entire functions represented by Laplace–Stieltjes transform converges on the whole complex plane and obtain some equivalence conditions about proximate growth of Laplace–Stieltjes transforms with finite order and infinite order. In addition, we also investigate the approximation of Laplace–Stieltjes transform with the proximate order and obtain some results containing the proximate growth order, the error, An∗, and λn, which are the extension and improvement of the previous theorems given by Luo and Kong and Singhal and Srivastava.

Rate of approximation of entire functions by a complete Dirichlet system

1984 ◽  
Vol 36 (6) ◽  
pp. 928-931
Author(s):  
V. Kh. Musoyan
Keyword(s):  
Entire Functions ◽  
Rate Of Approximation
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