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Fourier coefficients and partial sum of Fejer

  1. Oct 10, 2013 #1
    1. The problem statement, all variables and given/known data
    f(t) a continuously differentiable function twice over the circle T1
    cr its fourier coefficients and σn(f,t) partial sum of Fejer.
    a.Demonstrate that
    http://imageshack.us/a/img94/5992/ds35.png [Broken]


    b. Consider k as -n≤k≤n , using cr coefficients calculate
    http://imageshack.us/a/img542/8306/7jz2.png [Broken]

    c. Consider a function gn= max | f(t)-σn(f,t) | t in the circle T1
    show that lim n*gn=0 n->∞
    f is constant


    2. Relevant equations



    3. The attempt at a solution
    I've calculated
    http://img9.imageshack.us/img9/7775/mz30.png [Broken]
    I end up with a +1.. the summation about f(t) is in relative numbers Z using fourier but here it is |r|>n is it from here that I can "delete" the +1 ?

    b. :confused:
    c. :confused:
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 11, 2013 #2
    a. b. solved !!

    c. ....
     
    Last edited: Oct 11, 2013
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