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This paper studies a family of operators dependent on a small parameter ε > 0, which arise in a problem in fluid mechanics. It is shown that the spectra of the operators converge to  N  as ε → 0, even though, for every fixed ε > 0, the eigenvalues λ ε,  n   diverge quadratically as  n  → ∞.

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