broegger
Sep13-04, 04:07 AM
I really can't figure this one out: (\mathcal{T} is the circle [0;2\pi], \hat{f}(r) denotes the r'th Fourier coefficient of f and * denotes complex conjugation)
i) If f: \mathcal{T} \rightarrow \mathcal{C} is continous and g = Re(f) show that \hat{g}(r) = (\hat{f}(r) + \hat{f}(-r)^*)/2.
ii) Find the Fourier coefficients of Im(f).
i) If f: \mathcal{T} \rightarrow \mathcal{C} is continous and g = Re(f) show that \hat{g}(r) = (\hat{f}(r) + \hat{f}(-r)^*)/2.
ii) Find the Fourier coefficients of Im(f).