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May 28, 2019 at 2:19 comment added Matthias Ludewig Thanks Igor, that's completely right.
May 25, 2019 at 8:19 comment added Igor Khavkine It should be noted that the argument works as written for first order $Q$. If $Q$ is a differential operator of higher order, then the Green formula (aka integration by parts formula) just preceding $(*)$ needs to be adjusted and the change propagated through to all the orthogonality conditions.
Apr 25, 2019 at 7:28 history edited Matthias Ludewig CC BY-SA 4.0
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Apr 24, 2019 at 21:00 comment added Eugene Rabinovich Thank you for your answer, Matthias! What is the standard argument that shows that $\ker(D)=\ker(Q)\cap \ker(Q^*)$? The only one I can think of uses the formal self-adjointness of $D$, which fails to hold in this case.
Apr 24, 2019 at 5:14 history edited Matthias Ludewig CC BY-SA 4.0
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Apr 24, 2019 at 4:17 history answered Matthias Ludewig CC BY-SA 4.0