Homework Statement
Find the eigenvalues and a corresponding system of eigenvectors of the operator
Af(x) := Integration from 0 to 1 K(x; y)f(y) dy
where
K(x; y) = cos (2pi(x - y))
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!
Hey guys, i am studying cohomology by hatcher's. Could anyone provide me some ideas on these problems? Thank you all!
Let f : S2n-1 -> Sn denote a continuous map. Let Xf = D2n union f Sn be the space obtained by attaching a 2n-dim cell to Sn using the map f.
i). Calculate the integral...
Hey guys, i am studying cohomology by hatcher's. Could anyone provide me some ideas on these problems? Thank you!
Let f : S2n-1 -> Sn denote a continuous map. Let Xf = D2n union f Sn be the space obtained by attaching a 2n-dim cell to Sn using the map f.
i). Calculate the integral...