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We prove that the eigenvalues of a certain highly non‐self‐adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self‐adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ± ∞ . We use this result to determine the asymptotic distribution of the eigenvalues.

CORRESPONDENCE OF THE EIGENVALUES OF A NON‐SELF‐ADJOINT OPERATOR TO THOSE OF A SELF‐ADJOINT OPERATOR