Convergence of eigenvalues for a highly non-self-adjoint differential operator

Abstract

In this paper we study a family of operators dependent on a small parameter $\epsilon >0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed $\epsilon >0$, the eigenvalue asymptotics are quadratic.

16 pages

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