Boundedness and slow growth conditions along the real hyperplane for entire functions of exponential type

1989 ◽  
Vol 29 (4) ◽  
pp. 615-625
Author(s):  
V. N. Logvinenko
Keyword(s):  
Exponential Type ◽  
Slow Growth ◽  
Entire Functions ◽  
Growth Conditions ◽  
The Real ◽  
Functions Of Exponential Type ◽  
Real Hyperplane

Representation Formulas for Integrable and Entire Functions of Exponential Type II

1991 ◽  
Vol 43 (1) ◽  
pp. 34-47 ◽  
Author(s):  
Clément Frappier
Keyword(s):  
Entire Function ◽  
Real Axis ◽  
Exponential Type ◽  
Entire Functions ◽  
Type Ii ◽  
The Real ◽  
Representation Formulas ◽  
Functions Of Exponential Type ◽  
Image Position

We adopt the terminology and notations of [5]. If f ∈ Bτ is an entire function of exponential type τ bounded on the real axis then we have the complementary interpolation formulas [1, p. 142-143] andwhere t, γ are reals and

Approximation of locally integrable functions on the real line

2014 ◽  
Vol 12 (05) ◽  
pp. 1461002
Author(s):  
Xirong Chang
Keyword(s):  
Exponential Type ◽  
Real Line ◽  
Entire Functions ◽  
The Real ◽  
Integrable Functions ◽  
Functions Of Exponential Type

The aim of this paper is to extend (ψ, β)-derivatives to [Formula: see text]-derivatives for locally integrable functions on the real line and then investigate problems of approximation of the classes of functions determined by these derivatives with the use of entire functions of exponential type.

Inequalities for Entire Functions of Exponential Type

1984 ◽  
Vol 27 (4) ◽  
pp. 463-471 ◽  
Author(s):  
Clément Frappier
Keyword(s):  
Entire Function ◽  
Real Axis ◽  
Exponential Type ◽  
Entire Functions ◽  
Indicator Function ◽  
Trigonometric Polynomials ◽  
Bernstein’S Inequality ◽  
The Real ◽  
Functions Of Exponential Type ◽  
Image Position

AbstractBernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis thenGenchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, thenUsing a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.

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