2. Consider the compact operator on L[0, 27] defined by 27 1 Ku(x) = k(x y)u(y)dy, 27 where k(x) E L[0, 27] has period 27. Find the resolvent kernel function rx (x,y) in terms of the Fourier series k(x) = { cheine nez Recall that the resolvent kernel function is the kernel for the operator Jy, where (I \K)-1 = I +1Jx. As a check on your work, verify that J + K as 1+0. 2. Consider the compact operator on L[0, 27] defined by 27 1 Ku(x) = k(x y)u(y)dy, 27 where k(x) E L[0, 27] has period 27. Find the resolvent kernel function rx (x,y) in terms of the Fourier series k(x) = { cheine nez Recall that the resolvent kernel function is the kernel for the operator Jy, where (I \K)-1 = I +1Jx. As a check on your work, verify that J + K as 1+0