The Numerical Range in Banach Algebras and Complex Functions of Exponential type

1971 ◽  
Vol 3 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Béla Bollobás
Keyword(s):  
Exponential Type ◽  
Numerical Range ◽  
Banach Algebras ◽  
Functions Of Exponential Type ◽  
Complex Functions

scholarly journals Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra

1993 ◽  
Vol 35 (3) ◽  
pp. 325-326
Author(s):  
M. J. Crabb ◽  
C. M. McGregor
Keyword(s):  
Exponential Type ◽  
Line Segment ◽  
Convex Set ◽  
Numerical Range ◽  
Compact Convex ◽  
Banach Algebras ◽  
Functions Of Exponential Type ◽  
Compact Convex Set ◽  
Unital Banach Algebra ◽  
Extremal Algebra

For any compact convex set K ⊂ ℂ there is a unital Banach algebra Ea(K) generated by an element h in which every polynomial in h attains its maximum norm over all Banach algebras subject to the numerical range V(h) being contained in K, [1]. In the case of K a line segment in ℝ, we show here that Ea(K) does not have Arens regular multiplication. We also show that ideas about Ea(K) give simple proofs of, and extend, two inequalities of C. Frappier [4].

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.

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.

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