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

John Weir

doi:10.1112/s0025579310000616

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arXiv · 0801.4959

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

John Weir

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Abstract

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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BibTeX RIS

John Weir. 2008-08-26. Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator. https://doi.org/10.1112/s0025579310000616

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