# Fourier coefficients and partial sum of Fejer

1. Oct 10, 2013

### Dassinia

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.
c.

Last edited by a moderator: May 6, 2017
2. Oct 11, 2013

### Dassinia

a. b. solved !!

c. ....

Last edited: Oct 11, 2013