Borel Transform in the Class W of Quasi-entire Functions

2017 ◽  
Vol 12 (3) ◽  
pp. 571-587 ◽  
Author(s):  
Alexander P. Kerzhaev ◽  
Mikhail D. Kovalenko ◽  
Irina V. Menshova
Keyword(s):  
Entire Functions ◽  
Borel Transform

scholarly journals Holomorphy types and the Fourier-Borel transform between spaces of entire functions of a given type and order defined on Banach spaces

2012 ◽  
Vol 110 (1) ◽  
pp. 111 ◽  
Author(s):  
Vinícius V. Fávaro ◽  
Ariosvaldo M. Jatobá
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Entire Functions ◽  
Topological Isomorphism ◽  
Prime Type ◽  
Borel Transform ◽  
Holomorphy Types

Let $E$ be a Banach space and $\Theta$ be a $\pi_{1}$-holomorphy type. The main purpose of this paper is to show that the Fourier-Borel transform is an algebraic isomorphism between the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type strictly less than $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime},0,(\lambda (k) A)^{-1}}^{k^{\prime}}(E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type less than or equal to $(\lambda(k)A)^{-1}$. The same is proved for the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type less than or equal to $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime}, (\lambda(k)A)^{-1}}^{k^{\prime}}( E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type strictly less than $(\lambda(k)A)^{-1}$. Moreover, the Fourier-Borel transform is proved to be a topological isomorphism in certain cases.

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

scholarly journals Uniqueness on entire functions and their nth order exact differences with two shared values

2020 ◽  
Vol 18 (1) ◽  
pp. 211-215
Author(s):  
Shengjiang Chen ◽  
Aizhu Xu
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shared Values ◽  
Simple Method ◽  
Exact Difference ◽  
Hyper Order

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

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