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Continuous fourier

  1. May 27, 2014 #1
    Can someone tell me if the continuous fourier transform of a continuous (and vanishing fast enough ) function is also a continuous function?
  2. jcsd
  3. May 27, 2014 #2
    I can tell you more: in fact, if [itex]f \in L^{1}(\mathbb R)[/itex] then its Fourier Transform is uniformly continuous.
    Last edited: May 27, 2014
  4. May 28, 2014 #3
    Thanks very much but can u ... remind me which functions belong to L1(R)?
  5. May 28, 2014 #4


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    It are all the functions ##f:\mathbb{R}\rightarrow \mathbb{R}## which are absolutely integrable. That is, for which

    [tex]\int_{-\infty}^{+\infty} |f(x)|dx[/tex]

    is finite (and the integral makes sense).
  6. May 28, 2014 #5
    Thx again.
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