The Choquet boundary and approximation theory

Many of the classical theorems in approximation theory can be formulated in terms of convergence of a sequence of linear operators to the identity operator. To illustrate this, we consider one example in detail, obtaining Bernstein's proof of the Weierstrass approximation theorem. For each n ≥...

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Bibliographic Details
Main Author: Phelps, Robert R
Format: Book Chapter
Language:English
Online Access:Get full text
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Summary:Many of the classical theorems in approximation theory can be formulated in terms of convergence of a sequence of linear operators to the identity operator. To illustrate this, we consider one example in detail, obtaining Bernstein's proof of the Weierstrass approximation theorem. For each n ≥ 1, define the operator Bn from C[0,1] into the polynomials of degree at most n by setting, for f ∈ C[0,1].
ISSN:0075-8434
DOI:10.1007/3-540-48719-0_9