Find spectrum of the operator

287 Views Asked by At

I need some help to find point spectrum, residual spectrum, continuous spectrum and for this problem.

Let $\theta \in\mathbb{C}$. On the complex space $L^2[-1,1]$ consider the operator

$Au=v,$ where $v(x)=xu(x)+\theta \int^1_{-1} u(s)ds $.