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Dassinia

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## Homework Statement

f(t) a continuously differentiable function twice over the circle T

^{1}

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.

c.

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