Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

Details Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

2008-01-31

arxiv.org/abs/0801.4959v2

Mathematics

Spectral Theory

29 pages, corrections to section 3, added section 5

Scientific paper

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.

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