What Conditions Make This Differential Operator Self-Adjoint?

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The discussion centers on determining the conditions under which the differential operator O, defined as the sum of real functions f_n(x) multiplied by their respective derivatives, is self-adjoint. The operator is subject to specific boundary conditions: y(0)=y'(0)=y(1)=y'(1)=0. Participants emphasize the importance of understanding the definition of "self-adjoint" as a foundational step in solving the problem. The original poster expresses confusion and seeks guidance on the necessary constraints for the functions f_n. Clarifying the self-adjoint criteria is essential for progressing in this mathematical inquiry.
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Homework Statement



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.

Homework Equations


See above.

The Attempt at a Solution


Totally clueless. Please help.
 
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Well, what is the definition of "self adjoint"? That would be a good place to start.
 

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