We give a mathematically rigorous analysis which confirms the surprising results in a recent paper of Benilov, O‘Brien and Sazonov [ J. Fluid Mech . 497 (2003) 201-224] about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics. We also show that the set of eigenvectors does not form a basis for the operator.
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E. B. Davies (2007) studied this question.
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