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Math Help - Fourier series (pointwise convergence)

  1. #1
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    Fourier series (pointwise convergence)

    I have 3 functions on [-pi,pi[ and i need to describe why the fourier series converges pointwise on [-pi,pi], determine its sumfunction on [-pi,pi] and find out if it's also converges uniformly on [-pi,pi]

    the functions are as follows:

    1) f(x)= 1 for x in [pi/2,pi[ and 0 for x in [-pi,pi/2[


    2) g(x)= |x-pi/2|+|x+pi/2|

    3) h(x)= |x+pi/2|

    Honestly im a bit lost

    Anyway i think they're all piecewise differential c1 functions, and 1) at least is discontinious in -pi and pi.
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  2. #2
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    Quote Originally Posted by Zaph View Post
    I have 3 functions on [-pi,pi[ and i need to describe why the fourier series converges pointwise on [-pi,pi], determine its sumfunction on [-pi,pi] and find out if it's also converges uniformly on [-pi,pi]

    the functions are as follows:

    1) f(x)= 1 for x in [pi/2,pi[ and 0 for x in [-pi,pi/2[


    2) g(x)= |x-pi/2|+|x+pi/2|

    3) h(x)= |x+pi/2|

    Honestly im a bit lost

    Anyway i think they're all piecewise differential c1 functions, and 1) at least is discontinious in -pi and pi.
    1) At a jump discontinuity what does the Fourier series converge to?

    I think you are supposed to look up in your notes or the text book the convergence properties of Fourier series.

    CB
    Last edited by CaptainBlack; June 5th 2010 at 02:03 AM.
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  3. #3
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    Aye you're most likely right, I'll try look some more into it, but i seem to be doing something wrong.

    I guess i need to check if the function is piecewise differentiable, cause if it is and has a period of 2pi then it should converge pointwise?

    Thanks
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