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

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 +/-infinity. We use this result to determine the asymptotic distribution of the eigenvalues.