Possible Duplicate:
Eigenvalues of an operator
Find all the functions $f \in C([0,\frac{\pi}{2}])$ which are solutions of $ f(x) = \lambda \int_0^{\pi/2} \cos({x-y)}f(y)\,dy, \qquad \lambda \in \mathbb R. $
I just tried some algebraic manipulations and calculations, but I do not know ho to face this problem. Any help or hint is welcomed. Thanks a lot.