L_2[0,pi] is the Hilbert space of complex square integrable functions on [0,pi] and D={f belongs to L_{2}[0,pi] : f is twice continuously differentiable and f(0)=f(pi)=0)}.
let L :--> L_2[0,pi] be the sturm-Liouville operator Lf=-(e^xf')'
show that <Lf,f>\geq0 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