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Fourier coefficients and partial sum of Fejer

  • Thread starter Dassinia
  • Start date
  • #1
144
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Homework Statement


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


Homework Equations





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:
 
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Answers and Replies

  • #2
144
0
a. b. solved !!

c. ....
 
Last edited:

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