Recent content by 220205

  1. 2

    What are the Eigenvectors of the Integration Operator with Cosine Kernel?

    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))
  2. 2

    Prove Lim N→∞ of Rudin Fourier Series 8.19

    Thanks!
  3. 2

    Prove Lim N→∞ of Rudin Fourier Series 8.19

    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!