%0 Journal Article
%T Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator
%A John Weir
%J Mathematics
%D 2008
%I arXiv
%R 10.1112/S0025579310000616
%X 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 $\pm \infty$. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of the eigenvalues numerically. We compare these to earlier calculations by other authors.
%U http://arxiv.org/abs/0801.4959v2