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Spectral analysis of the Fox--Li operator

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In this talk I present some recent work with Prof. Arieh Iserles on the asymptotic behavior of a generic eigenvalue and eigenfunction pair of the Fox—Li operator in the asymptotic regime of large oscillations. This Fox—Li eigenvalue and eigenfunction problem is particularly relevant to the science of laser beams and resonators, as well as a very appealing theme for research given that it is (mildly) non-normal and falls outside of standard spectral theory. The talk will concern two different approaches (which relate to two different ways of approximating the eigenfunctions: either in inverse powers of large oscillation or in Fourier basis) and conclude with current thoughts on the problem.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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