1. Sep 28, 2011

### MarkovMarakov

1. The problem statement, all variables and given/known data

When is the following operator self-adjoint? I am looking for constraints on $f_n$'s s.t. The operator below becomes self-adjoint.

$O:= \sum_{n=0}^4 f_n(x){d^n\over dx^n}$ subjected to boundary conditions $y(0)=y'(0)=y(1)=y'(1)=0$ and where $f_n$'s are real functions.

Thanks.

2. Relevant equations
See above.

3. The attempt at a solution