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Square integrable question

  1. Oct 24, 2006 #1


    is square integrable, why does

    [tex]\int_a^b \frac{f(x)}{x} \sin{nx} dx \longrightarrow 0[/tex]


    [tex]n \rightarrow \infty[/tex]

    Last edited: Oct 24, 2006
  2. jcsd
  3. Oct 24, 2006 #2


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    This is not an answer, but maybe a hint is contained in here. I think there is some theorem that will let you prove a square integrable function on a finite interval is absolutely integrable on that interval, and that demands a certain smoothness of the function. The integral of any smooth function multiplied by an infinite frequency sinusoid must be zero.
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