Hello

is the Hilbert space of complex square integrable functions on [0,pi] and D={f belongs to : f is twice continuously differentiable and f(0)=f(pi)=0)}.

let L :--> be the sturm-Liouville operator

show that for all f in D. Further, show that all eigenvalues of L are positive.

Can you please give me some hits on how to do this as I have final exam on this topic tomorrow morning.

many thanks