1. May 10, 2009 #1

   Niles

   

   1. The problem statement, all variables and given/known data
   HI all.
   
   In order to perform a Fourier transform on a function f(x), f(x) must be integrable, i.e.
   
   [tex]
   \int_{-\infty}^{\infty}|f(x)|dx < \infty.
   [/tex]
   
   Can you confirm that this also implies that f(x) -> 0 for x -> (+/-) infinity?

    

   Niles, May 10, 2009
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3. May 10, 2009 #2

   Cyosis

   

   Homework Helper

   Can you find a function that has a finite area beneath it while not being zero in infinity?

    

   Cyosis, May 10, 2009
4. May 10, 2009 #3

   Niles

   

   No. But I am wondering if it is a sufficient conditions for the integral to be finite? E.g. f(x) = x^-1?

    

   Niles, May 10, 2009
5. May 10, 2009 #4

   Cyosis

   

   Homework Helper

   To avoid any confusion. Do you mean if f(x)->0 when x->+-infinity then the integral of f(x) over +- infinity converges? This is not true and you already gave a counter example. The function x^-1 goes to zero, but the integral of x^-1 from -infinity to infinity diverges.

    

   Cyosis, May 10, 2009
6. May 10, 2009 #5

   Niles

   

   Great, thanks!

    

   Niles, May 10, 2009

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