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Expand in more localized than Fourier

  1. Feb 20, 2010 #1
    Can I expand a function in
    [tex]f(x)=\sum_k g_k(x\cdot k)[/tex]
    where g is a periodic function that is not an exponential?
    So
    [tex]g_k(a)=g_k(a+1)[/tex]

    What if there doesn't necessarily have to be a back transformation or if the expansion doesn't have to be unique?
     
  2. jcsd
  3. Feb 21, 2010 #2

    jasonRF

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    Science Advisor
    Gold Member

    If g is a periodic function, then you can represent it with a Fourier series. So if g is not an exponential, it is a (most likely infinite) sum of exponentials.
     
  4. Feb 21, 2010 #3
    So can I find a function for g? I thought if g is a combination of exponentials, then there won't be another solution rather than the usual Fourier transform?
     
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