Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane

1995 ◽  
Vol 58 (3) ◽  
pp. 921-927
Author(s):  
A. A. Dovgoshei
Keyword(s):  
Complex Plane ◽  
Polynomial Approximation ◽  
Entire Functions ◽  
Compact Sets ◽  
Uniform Polynomial Approximation

Weighted Polynomial Approximation of Entire Functions on Unbounded Subsets of the Complex Plane

1993 ◽  
Vol 36 (3) ◽  
pp. 303-313 ◽  
Author(s):  
H. N. Mhaskar
Keyword(s):  
Asymptotic Behavior ◽  
Complex Plane ◽  
Polynomial Approximation ◽  
Entire Functions ◽  
Weighted Approximation ◽  
Weighted Polynomial Approximation

AbstractWe study the asymptotic behavior of the n-widths of a class of entire functions in weighted approximation on subsets of the complex plane.

The Usual Behaviour of Rational Approximations

1983 ◽  
Vol 26 (3) ◽  
pp. 317-323 ◽  
Author(s):  
Peter B. Borwein
Keyword(s):  
Complex Plane ◽  
Metric Space ◽  
Unit Disc ◽  
Entire Functions ◽  
Complete Metric Space ◽  
Point Of View ◽  
Rational Approximations ◽  
Speed Of Convergence ◽  
Entire Plane ◽  
Categorical Point

AbstractQuestions concerning the convergence of Padé and best rational approximations are considered from a categorical point of view in the complete metric space of entire functions. The set of functions for which a subsequence of the mth row of the Padé table converges uniformly on compact subsets of the complex plane is shown to be residual.The speed of convergence of best uniform rational approximations and Padé approximations on the unit disc is compared. It is shown that, in a categorical sense, it is expected that subsequences of these approximants will converge at the same rate.Likewise, it is expected that the poles of certain sequences of best uniform rational approximations wil be dense in the entire plane.

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 .

Sign in / Sign up

Export Citation Format

Share Document