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View Full Version : help with Riemann-Lebesgue theorem pls


fourier jr
Oct21-04, 02:46 PM
If f is integrable on (-\infty, \infty) = E then \lim_{n\rightarrow\infty} \int_E f(x)cos(nx) = 0

it's supposed to be easy if f is a step function & then i can use another problem that was part of the homework, but i can't seem to figure out how that would work.....





(ps- maybe i shouldn't call myself fourier jr if i'm stuck on a problem like this :uhh: )

shmoe
Oct21-04, 06:16 PM
If f is a step function, break it up into the corresponding intervals. Can you show the integral restricted to any one of these intervals goes to zero as n goes to infinity?

fourier jr
Oct22-04, 04:17 AM
thx for the tip... :smile: i must have been thinking too hard about it... :redface: