Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Square integrable question

  1. Oct 24, 2006 #1
    If

    [tex]\frac{f(x)}{x}[/tex]

    is square integrable, why does

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

    when

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

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

    OlderDan

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook