# On determinants of integrable operators with shifts

Source: [On determinants of integrable operators with shifts](<https://www.sota2.com/research/paper/68fa50091e209131ce968531>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:38:39.238Z

Authors: A. R. Its, K. K. Kozlowski

Published: 2013-01-10T19:22:19.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1301.2221>)

[PDF](<https://arxiv.org/pdf/1301.2221.pdf>)