Approximation of analytic functions in some functional spaces and the rational approximation of functions from Hardy classes

1993 ◽  
Vol 53 (2) ◽  
pp. 158-162
Author(s):  
A. A. Dovgoshei
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Approximation Of Functions ◽  
Hardy Classes

scholarly journals On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Devendra Kumar
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Best Approximation ◽  
Maximum Modulus ◽  
Approximation Of Functions ◽  
The Best Approximation ◽  
Approximation Errors ◽  
Rate Of Decay ◽  
Rates Of Growth

The present paper is concerned with the rational approximation of functions holomorphic on a domainG⊂C, having generalized types of rates of growth. Moreover, we obtain the characterization of the rate of decay of product of the best approximation errors for functionsfhaving fast and slow rates of growth of the maximum modulus.

On Padé and Best Rational Approximation

1983 ◽  
Vol 26 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Peter B. Borwein
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Unit Disc ◽  
Padé Approximants ◽  
Main Diagonal ◽  
Rational Approximations ◽  
Pade Approximants ◽  
Best Rational Approximation

AbstractIt is reasonable to expect that, under suitable conditions, Padé approximants should provide nearly optimal rational approximations to analytic functions in the unit disc. This is shown to be the case for ez in the sense that main diagonal Padé approximants are shown to converge as expeditiously as best uniform approximants. Some more general but less precise related results are discussed.

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