Accession Number : ADA118974
Title : Polynomial Approximation: The Weierstrass Approximation Theorem.
Descriptive Note : Master's thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
Personal Author(s) : Nichols,Shirley Jo
PDF Url : ADA118974
Report Date : Aug 1982
Pagination or Media Count : 31
Abstract : In this paper we will look at three proofs of the Weierstrass Approximation Theorem. The first proof is in much the same form in which Weierstrass originally proved his theorem. The next is due to Lebesgue. It is by far the easiest proof to follow, with only a minimum knowledge of analysis required. The last arises from probability and uses the Bernstein polynomials. Secondly we look at a generalization of this theorem, called the Stone-Weierstrass Theorem. This generalization was inspired by modern developments in mathematics. The theorem deals with functions on a general compact space rather than on a closed interval.
Descriptors : *Polynomials, *Approximation(Mathematics), Continuity, Functions(Mathematics), Probability, Intervals, Theorems, Theses
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE