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Integrable integral operator can be studied by means of a matrix Riemann–Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann–Hilbert problem becomes operator-valued and this complicates strongly the analysis. In this note, we show how to circumvent, in a very simple way, the use of such a setting while still being able to characterize the large- x  asymptotic behavior of the determinant associated with the operator.

On Determinants of Integrable Operators with Shifts