
Fourier Series
Hey there everyone... I realy need your help in the following questions in Fourier Series:
1. Prove that the fourier series of f(x)=x at (pi,pi) pointwise converges but not uniformly converges (You should do it without calculate the series!)
2. Prove that if f(x) is continous, even and periodic with a period of 2pi and for each n=0,1,2,3... : Integral_from 0 to pi_ f(x)*cos(nx) dx = 0 then f(x)=0 . Hint: You should use parsbel equality.
3. Is there any continous function at [pi,pi] such as the series Sigma_n=2 to infinity_ [sin(nx)/sqrt(ln(n)) ] is her fourier series?
Thanks in advance...