- #1
s_j_sawyer
- 21
- 0
Homework Statement
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,...
Homework 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.
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?