Abstract
We establish conditions for orthogonality of eigenvectors and the type of eigenvalues (real or purely imaginary) of an operator pair A, B in an equation Au + λBu = 0which permute (or skew-permute) with a given third operator. We consider equations with differential operators A and B (the differential spectral problem), with a differential operator A and an integro-differential operator B, and also with algebraic operators A and B.
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