When is the following operator self-adjoint?(Is there a difference between self-adjoint and Hermitian?)
$O:= \sum_{n=0}^4 f_n(x){d^n\over dx^n}$ subjected to boundary conditions $y(0)=y'(0)=y(1)=y'(1)=0$ and where $f_n$'s are real functions.
Thanks.