Unconditional bases of Hilbert spaces composed of values of entire vector functions of exponential type

1999 ◽  
Vol 33 (1) ◽  
pp. 52-55 ◽  
Author(s):  
G. M. Gubreev
Keyword(s):  
Exponential Type ◽  
Hilbert Spaces ◽  
Unconditional Bases ◽  
Functions Of Exponential Type ◽  
Entire Vector

FUNCTIONS OF EXPONENTIAL TYPE NOT VANISHING IN A HALF-PLANE

Analysis ◽  
1997 ◽  
Vol 17 (4) ◽  
pp. 395-402 ◽  
Author(s):  
Robert Gardner ◽  
N. K. Govil
Keyword(s):  
Half Plane ◽  
Exponential Type ◽  
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.

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