Smallest plurisuperharmonic majorant and multipliers of entire functions. II. Algebras of functions of finite ?-type

1992 ◽  
Vol 33 (3) ◽  
pp. 519-524
Author(s):  
B. N. Khabibullin
Keyword(s):  
Finite Type ◽  
Entire Functions

Weak-Star Continuous Analytic Functions

1995 ◽  
Vol 47 (4) ◽  
pp. 673-683 ◽  
Author(s):  
R. M. Aron ◽  
B. J. Cole ◽  
T. W. Gamelin
Keyword(s):  
Unit Ball ◽  
Finite Type ◽  
Analytic Functions ◽  
Approximation Property ◽  
Entire Functions ◽  
Open Unit ◽  
Closed Unit Ball ◽  
Open Unit Ball ◽  
Weakly Continuous ◽  
Weak Star

AbstractLet 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximation of entire functions by finite-type polynomials. Assuming 𝒳* has the approximation property, we show that entire functions are approximable uniformly on bounded sets if and only if the spectrum of the algebra of entire functions coincides (as a point set) with 𝒳**.

scholarly journals Kernel convergence of hyperbolic components

1997 ◽  
Vol 17 (5) ◽  
pp. 1137-1146 ◽  
Author(s):  
BERND KRAUSKOPF ◽  
HARTJE KRIETE
Keyword(s):  
Finite Type ◽  
Parameter Space ◽  
Entire Functions ◽  
Kernel Convergence

We study families $G(\lambda,\cdot)$ of entire functions that are approximated by a sequence of families $G_n(\lambda,\cdot)$ of entire functions, where $\lambda\in\C$ is a parameter. In order to control the dynamics, the families are assumed to be of the same constant finite type. In this setting we prove the convergence of the hyperbolic components in parameter space as kernels in the sense of Carathéodory.

scholarly journals On the best mean-square approximation by entire functions of finite type on the line

2021 ◽  
Vol 17 ◽  
pp. 36
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Finite Type ◽  
Entire Functions ◽  
Jackson Type ◽  
Mean Square ◽  
Differentiable Functions

Jackson-type inequalities have been obtained for the best mean square approximation of differentiable functions by means of the entire functions of finite type on the line.

scholarly journals Approximation of entire functions over Carathéodory domains

1982 ◽  
Vol 25 (2) ◽  
pp. 221-229 ◽  
Author(s):  
G.P. Kapoor ◽  
A. Nautiyal
Keyword(s):  
Entire Function ◽  
Analytic Continuation ◽  
Finite Type ◽  
Finite Order ◽  
Jordan Curve ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Image Position ◽  
Necessary And Sufficient

Let D be a domain bounded by a Jordan curve. For 1 ≤ p ≤ ∞, let Lp(D) be the class of all functions f holomorphic in D such that where A is the area of D. For f ∈Lp(D), setπn consists of all polynomials of degree at most n. Recently, Andre Giroux (J. Approx. Theory 28 (1980), 45–53) has obtained necessary and sufficient conditions, in terms of the rate of decrease of the approximation error , such that has an analytic continuation as an entire function having finite order and finite type. In the present paper we have considered the approximation error (*) on a Carathéodory domain and have extended the results of Giroux for the case 1 ≤ p < 2.

scholarly journals Weighted Frechet spaces of entire functions from the class of power series spaces of finite type

2013 ◽  
Author(s):  
П.С. Сергунин ◽  
А.В. Абанин ◽  
Ч.Т. Фам
Keyword(s):  
Power Series ◽  
Finite Type ◽  
Entire Functions ◽  
Fréchet Spaces

Изучаются весовые пространства Фреше целых функций, задаваемые весовыми последовательностями общего вида. Получены достаточные условия на веса, при которых они обладают топологическими инвариантами Фогта - Вагнера, и, таким образом, относятся к классу пространств степенных рядов конечного типа.

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