November 22nd, 2009, 12:40 PM  #1 
Newbie Joined: Nov 2009 Posts: 9 Thanks: 0  help me or give ideal
I am using the fejercesaro 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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
the zero set of an ideal  rayman  Abstract Algebra  1  January 28th, 2014 11:35 PM 
Ideal in z(x)  alejandrofigueroa  Abstract Algebra  0  November 4th, 2013 09:11 AM 
ideal  ely_en  Real Analysis  0  March 4th, 2012 11:22 AM 
Two likes give a negative, two unlikes give positive  WHY?  sharp  Elementary Math  3  October 27th, 2010 03:36 PM 
Ideal  HairOnABiscuit  Abstract Algebra  3  December 12th, 2009 01:11 PM 