Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spectral method related

  1. Jun 19, 2010 #1

    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. jcsd
  3. Jun 19, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook