Expand in more localized than Fourier

  • Thread starter Gerenuk
  • Start date
  • #1
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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?
 

Answers and Replies

  • #2
jasonRF
Science Advisor
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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.
 
  • #3
1,015
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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