# Spectral method related

1. Jun 19, 2010

### defunc

Hi

In the spectral method, the fourier series is differentiated term by term. How do we know this series converges uniformly to the real derivative? Or can it be shown in general for fouries series?

Thanks a lot!

2. Jun 19, 2010

### jbunniii

It is NOT true in general that you can differentiate a Fourier series term by term. There is a counterexample at this link (PDF file) along with some conditions under which termwise differentiation is OK:

http://www.mth.pdx.edu/~daescu/mth410_510w/Fourier_series.pdf [Broken]

Last edited by a moderator: May 4, 2017