Given the following fredholm integral equation $g(s) =f(s)+\lambda\int_{0}^{2 \pi}sin(t+s) g(t) dt$ defined from $C[0,2\pi]$ over itself. Show that if $f(s) =s$ then the equation doesn't have solution ¿what about $f(s) =1$?.
Hi, I need to prove this problem using fredholm theorems (the ones that relate the primal no homogeneous equation with the dual homogeneous equation and viceversa) and I don't understand those theorems yet.