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Rudin 8.19
f is a continuous function on R, f(x+2Pi)=f(x), and a/pi is irrational.
Prove that
lim N goes to infinity (Sum n=1,...,N f(x+na)) =(1/2pi) * [tex]\int[/tex] f(t)dt from -pi to pi
for every x.
Hint: do it first for f(x)=exp(ikx)
THANKS!
f is a continuous function on R, f(x+2Pi)=f(x), and a/pi is irrational.
Prove that
lim N goes to infinity (Sum n=1,...,N f(x+na)) =(1/2pi) * [tex]\int[/tex] f(t)dt from -pi to pi
for every x.
Hint: do it first for f(x)=exp(ikx)
THANKS!
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