The Weierstrass approximation theorem for maps between real algebraic varieties

1999 ◽  
Vol 314 (4) ◽  
pp. 601-612 ◽  
Author(s):  
J. Bochnak ◽  
W. Kucharz
Keyword(s):  
Approximation Theorem ◽  
Algebraic Varieties ◽  
Real Algebraic Varieties ◽  
Weierstrass Approximation Theorem

Real algebraic varieties and cobordism

2007 ◽  
Vol 71 (3) ◽  
pp. 573-601
Author(s):  
Vyacheslav A Krasnov
Keyword(s):  
Algebraic Varieties ◽  
Real Algebraic Varieties

Bernstein Power Series

1964 ◽  
Vol 16 ◽  
pp. 241-252 ◽  
Author(s):  
E. W. Cheney ◽  
A. Sharma
Keyword(s):  
Power Series ◽  
Infinite Series ◽  
Approximation Theorem ◽  
Bernstein Polynomials ◽  
Starting Point ◽  
Image Position ◽  
Weierstrass Approximation Theorem

In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomialsare constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared. It is our purpose here to consider several generalizations in the form of infinite series and to establish some of their properties.

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