Self-Adjointness on Differential Equations

"Self-Adjointness" on Differential Equations

Hey, Im just wondering why is that we always try to look for self-adjoints Differential Equations. I mean I know the advantages of having self-adjoint operators, i.e, they have real eigenvalues, eigenfunctions are orthogonal and form a complete set. But, Im having a hard time trying to relate this to solving actual differential equations, can you give me quick tips or ideas on this? or what should I look for?... Thanks.
 

HallsofIvy

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Re: "Self-Adjointness" on Differential Equations

Those are the reasons! The differential operators of a self adjoint differential equations are self adjoint transformations so there exist a basis for the solution space consisting of "eigenfunctions" of those operators and it becomes easy to find the solution.
 

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