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Math Help - How to be sure that a serie isn't a fourier series of a derivable function

  1. #1
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    How to be sure that a serie isn't a fourier series of a derivable function

    Hi there. I have this interesting problem which I don't know how to solve. I'll post it here because I think more people will se it, but I'm not sure if this is the proper subforum.

    The problem says: How can be sure that \sum_{n = 1}^\infty \frac{1}{n}\sin (nx) isn't the Fourier series of a derivable function?

    I thought that it doesn't accomplish the Diritchlet postulates, but it actually doesn't mean that it isn't a fourier series.

    Does anyone know how to solve this?

    Bye there and thanks.
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  2. #2
    Super Member girdav's Avatar
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    If f is the function which is represented by this series and derivable, use an integration by parts to compute the Fourier coefficients of f'. Use Parseval equality to show a contradiction.
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  3. #3
    A Plied Mathematician
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    Quote Originally Posted by Ulysses View Post
    ...Fourier series of a derivable function?...
    A better phrase would be "differentiable function", just for your information.
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