scholarly journals Best approximation of holomorphic functions from hardy space in terms of Taylor coefficients

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1417-1424
Author(s):  
F.G. Abdullayev ◽  
G.A. Abdullayev ◽  
V.V. Savchuk
Keyword(s):  
Hardy Space ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Holomorphic Functions ◽  
Best Polynomial Approximation ◽  
Taylor Coefficients

We describe the set of holomorphic functions from the Hardy space Hq, 1 ? q ? ?, for which the best polynomial approximation En(f)q is equal to |f (n)(0)|=n!.

scholarly journals A note on a space Hp, a of holomorphic functions

1987 ◽  
Vol 35 (3) ◽  
pp. 471-479
Author(s):  
H. O. Kim ◽  
S. M. Kim ◽  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Complex Plane ◽  
Unit Disc ◽  
Weak Type ◽  
Holomorphic Functions ◽  
Embedding Theorem ◽  
Type Operator ◽  
Taylor Coefficients ◽  
Bounded Holomorphic

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

scholarly journals Generalized Order and Best Approximation of Entire Function in -Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammed Harfaoui
Keyword(s):  
Entire Function ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Best Polynomial Approximation ◽  
Growth Of Entire Functions

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set , where is the Siciak extremal function of a -regular compact .

Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces

2002 ◽  
Vol 18 (4) ◽  
pp. 551-568 ◽  
Author(s):  
D. H. Kim ◽  
S. H. Kim ◽  
K. H. Kwon ◽  
Xin Li
Keyword(s):  
Polynomial Approximation ◽  
Best Polynomial Approximation
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