scholarly journals On sharp inequalities of Jackson type for entire functions in $L_2$

2021 ◽  
Vol 15 ◽  
pp. 89
Author(s):  
V.G. Doronin ◽  
A.A. Ligun
Keyword(s):  
Exponential Type ◽  
Entire Functions ◽  
Jackson Type ◽  
Functions Of Exponential Type

We conducted the research of sharp inequalities of Jackson type in $L_2$ space for approximation by entire functions of exponential type.

Representation Formulas for Integrable and Entire Functions of Exponential Type I

1988 ◽  
Vol 40 (04) ◽  
pp. 1010-1024 ◽  
Author(s):  
Clément Frappier
Keyword(s):  
Exponential Type ◽  
Entire Functions ◽  
Conjugate Function ◽  
Interpolation Formula ◽  
Type I ◽  
Additional Hypothesis ◽  
Period 2 ◽  
Representation Formulas ◽  
Functions Of Exponential Type ◽  
Image Position

Let Bτ denote the class of entire functions of exponential type τ (>0) bounded on the real axis. For the function f ∊ Bτ we have the interpolation formula [1, p. 143] 1.1 where t, γ are real numbers and is the so called conjugate function of f. Let us put 1.2 The function Gγ,f is a periodic function of α, with period 2. For t = 0 (the general case is obtained by translation) the righthand member of (1) is 2τGγ,f (1). In the following paper we suppose that f satisfies an additional hypothesis of the form f(x) = O(|x|-ε), for some ε > 0, as x → ±∞ and we give an integral representation of Gγ,f(α) which is valid for 0 ≦ α ≦ 2.

scholarly journals Inequalities and representation formulas for functions of exponential type

1995 ◽  
Vol 58 (1) ◽  
pp. 15-26
Author(s):  
C. Frappier ◽  
P. Olivier
Keyword(s):  
Exponential Type ◽  
Entire Functions ◽  
Representation Formula ◽  
Bernstein’S Inequality ◽  
Representation Formulas ◽  
Functions Of Exponential Type ◽  
Bernstein's Inequality

AbstractWe generalise the classical Bernstein's inequality: . Moreover we obtain a new representation formula for entire functions of exponential type.

Sign in / Sign up

Export Citation Format

Share Document