Prove Lim N→∞ of Rudin Fourier Series 8.19

220205
Messages
3
Reaction score
0
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) * \int f(t)dt from -pi to pi
for every x.

Hint: do it first for f(x)=exp(ikx)

THANKS!
 
Last edited:
Physics news on Phys.org
welcome to pf!

hi 220205! welcome to pf! :wink:

hint: do it first for f(x)=exp(ikx) :smile:
 


tiny-tim said:
hi 220205! welcome to pf! :wink:

hint: do it first for f(x)=exp(ikx) :smile:

Thanks!
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top