T is a bounded linear operator mapping from C[0,1] to C[0,1] with the two norm.
Find the non-zero eigenvalues of T, where
\(\displaystyle (Tf)(x)=\int_{a}^{b} f(t)(x+t)dt\)
You may assume all eigenvectors for non-zero eigenvalues are of the form \(\displaystyle f(x)=Ax+B\)
Find the non-zero eigenvalues of T, where
\(\displaystyle (Tf)(x)=\int_{a}^{b} f(t)(x+t)dt\)
You may assume all eigenvectors for non-zero eigenvalues are of the form \(\displaystyle f(x)=Ax+B\)