Consider the following linear mapping from C[-pi,pi] into itself:
L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi]. Here G(x), H(x) are given continuous functions. Find a function f such that L*f=lambda*f for some lambda and find the value of lambda. This is a generalization of the notion for particular case G(x)=cosx,H(x)=x^2. Hint Look for f(x)=aG(s). Explain why this assumption is reasonable.
A relation between functions is investigated. The solution is detailed and well presented.