1. Feb 20, 2010 #1

   Gerenuk

   

   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?

    

   Gerenuk, Feb 20, 2010
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3. Feb 21, 2010 #2

   jasonRF

   

   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.

    

   jasonRF, Feb 21, 2010
4. Feb 21, 2010 #3

   Gerenuk

   

   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?

    

   Gerenuk, Feb 21, 2010

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