(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy

|an| <= K/n and |bn| <= L/n n=1,2,...

2. Relevant equations

an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx

bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx

Sorry if my form is slightly unpleasing to the eye, but I'm sure if you're reading my post you probably know what I'm talking about.

3. The attempt at a solution

|an| = | 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx |

<= 1/pi * int[-pi..pi] | (f(x)*cos(nx)) | dx

and that's as far as I could get. I thought maybe I could show that

int[-pi..pi]( | cosnx | )dx <= (1/n)*int[-pi..pi]( |cosx| ) dx

but that turned out to be false.

Any ideas?

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# Homework Help: Fourier Coefficients Property

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