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 November 22nd, 2009, 12:40 PM #1 Newbie   Joined: Nov 2009 Posts: 9 Thanks: 0 help me or give ideal I am using the fejer-cesaro to prove the weierstrass theorem. I need help of finding this, "simply convert the given function f : [a, b] ? C into a symmetric function g over an interval of size 2(b ? a), identify the end points of the new interval so that it is isomorphic to T". I tried but I couldn't get the correct interval. "Weierstrass� Theorem says that given any continuous function over a ?nite inverval and an arbitrarily small envelope around it, we can ?nd a polynomial that ?ts inside that envelope in that interval. To see why this is implied by Fejer�s Theorem, simply convert the given function f : [a, b] ? C into a symmetric function g over an interval of size 2(b ? a), identify the end points of the new interval so that it is isomorphic to T, and use Fejer�s Theorem to conclude that ?n (g, .) is a trigonometric polynomial close to g (and hence f ). To see why Weierstrass� Theorem implies Fejer�s Theorem, recall that cos rt can be expressed as a degree r polynomial in cos t. Use this to express the promised trigonometric polynomial P (t) as a linear combination of cos rt and sin rt with ?n ? r ? n." Tags give, ideal Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rayman Abstract Algebra 1 January 28th, 2014 11:35 PM alejandrofigueroa Abstract Algebra 0 November 4th, 2013 09:11 AM ely_en Real Analysis 0 March 4th, 2012 11:22 AM sharp Elementary Math 3 October 27th, 2010 03:36 PM HairOnABiscuit Abstract Algebra 3 December 12th, 2009 01:11 PM

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